Open Document Format for Office Applications (OpenDocument) Version 1.2
Part 2: Recalculated Formula (OpenFormula) Format
OASIS Standard
29 September 2011
Specification URIs:
This version:
http://docs.oasisopen.org/office/v1.2/os/OpenDocumentv1.2ospart2.odt (Authoritative)
http://docs.oasisopen.org/office/v1.2/os/OpenDocumentv1.2ospart2.pdf
http://docs.oasisopen.org/office/v1.2/os/OpenDocumentv1.2ospart2.html
Previous version:
http://docs.oasisopen.org/office/v1.2/csd06/OpenDocumentv1.2csd06part2.odt (Authoritative)
http://docs.oasisopen.org/office/v1.2/csd06/OpenDocumentv1.2csd06part2.pdf
http://docs.oasisopen.org/office/v1.2/csd06/OpenDocumentv1.2csd06part2.html
Latest version:
http://docs.oasisopen.org/office/v1.2/OpenDocumentv1.2part2.odt (Authoritative)
http://docs.oasisopen.org/office/v1.2/OpenDocumentv1.2part2.pdf
http://docs.oasisopen.org/office/v1.2/OpenDocumentv1.2part2.html
Technical Committee:
OASIS Open Document Format for Office Applications (OpenDocument) TC
Chairs:
Rob Weir, IBM
Michael Brauer, Oracle Corporation
Editors:
David A. Wheeler
Patrick Durusau
Eike Rathke, Oracle Corporation
Rob Weir, IBM
Related work:
This document is part of the OASIS Open Document Format for Office Applications (OpenDocument) Version 1.2 specification.
The OpenDocument v1.2 specification has these parts:
OpenDocument v1.2 part 1: OpenDocument Schema
OpenDocument v1.2 part 2: Recalculated Formula (OpenFormula) Format (this part)
OpenDocument v1.2 part 3: Packages
Declared XML namespaces:
None.
Abstract:
This document is part of the Open Document Format for Office Applications (OpenDocument) Version 1.2 specification.
It defines a formula language to be used in OpenDocument documents.
Status:
This document was last revised or approved by the OASIS Open Document Format for Office Applications (OpenDocument) TC on the above date. The level of approval is also listed above. Check the "Latest version" location noted above for possible later revisions of this document.
Technical Committee members should send comments on this specification to the Technical Committee’s email list. Others should send comments to the Technical Committee by using the “Send A Comment” button on the Technical Committee’s web page at http://www.oasisopen.org/committees/office/.
For information on whether any patents have been disclosed that may be essential to implementing this specification, and any offers of patent licensing terms, please refer to the Intellectual Property Rights section of the Technical Committee web page (http://www.oasisopen.org/committees/office/ipr.php).
Citation format:
When referencing this specification the following citation format should be used:
OpenDocumentv1.2part2
Open Document Format for Office Applications (OpenDocument) Version 1.2 Part 2: Recalculated Formula (OpenFormula) Format. 29 September 2011. OASIS Standard. http://docs.oasisopen.org/office/v1.2/os/OpenDocumentv1.2ospart2.html
Notices
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Table of Contents
This document is part of the Open Document Format for Office Applications (OpenDocument) Version 1.2 specification. It defines a formula language for OpenDocument documents, which is also called OpenFormula.
OpenFormula is a specification of an open format for exchanging recalculated formulas between office applications, in particular, formulas in spreadsheet documents. OpenFormula defines data types, syntax, and semantics for recalculated formulas, including predefined functions and operations.
Using OpenFormula allows document creators to change the office application they use, exchange formulas with others (who may use a different application), and access formulas far in the future, with confidence that the recalculated formulas in their documents will produce equivalent results if given equivalent inputs.
OpenFormula is intended to be a supporting document to the Open Document Format for Office Applications (OpenDocument) format, particularly for defining its attributes table:formula and text:formula. It can also be used in other circumstances where a simple, easytoread infix text notation is desired for exchanging recalculated formulas.
All text is normative unless otherwise labeled.
Within the normative text of this specification, the terms "shall", "shall not", "should", "should not", "may" and “need not” are to be interpreted as described in Annex H of [ISO/IEC Directives].
OpenFormula defines:
1.data types
2.syntax
3.semantics
for recalculated formulas.
OpenFormula also defines functions.
OpenFormula does not define:
1.a user interface
2.a general notation for mathematical expressions
[CharModel] Martin J. Dürst, et. al., Character Model for the World Wide Web 1.0: Fundamentals, http://www.w3.org/TR/2005/RECcharmod20050215/, W3C, 2005.
[ISO/IEC Directives] ISO/IEC Directives, Part 2 (Fifth Edition) Rules for the structure and drafting of International Standards, International Organization for Standardization and International Electrotechnical Commission, 2004.
[ISO4217] ISO 4217:2008 Codes for the representation of currencies and funds, International Organization for Standardization and International Electrotechnical Commission, 2008.
[ISO8601] ISO 8601:2004 Data elements and interchange formats  Information interchange  Representation of dates and times, International Organization for Standardization and International Electrotechnical Commission, 2004.
[RFC3986] T. BernersLee, R. Fielding, L. Masinter, Uniform Resource Identifier (URI): Generic Syntax, http://www.ietf.org/rfc/rfc3986.txt, IETF, 2005.
[RFC3987] M. Duerst, M. Suignard, Internationalized Resource Identifiers (IRIs), http://www.ietf.org/rfc/rfc3987.txt, IETF, 2005.
[UNICODE] The Unicode Consortium. The Unicode Standard, Version 5.2.0, defined by: The Unicode Standard, Version 5.2 (Mountain View, CA, The Unicode Consortium, 2009. ISBN 9781936213009). (http://www.unicode.org/versions/Unicode5.2.0/).
[UTR15] Mark Davis, Martin Dürst, Unicode Normalization Forms, Unicode Technical Report #15, http://www.unicode.org/reports/tr15/tr1525.html, 2005.
[XML1.0] Tim Bray, Jean Paoli, C. M. SperbergMcQueen, Eve Maler, François Yergeau , Extensible Markup Language (XML) 1.0 (Fourth Edition), http://www.w3.org/TR/2006/RECxml20060816/, W3C, 2006.
[JISX0201] The Unicode Consortium., JIS X 0201 (1976) to Unicode 1.1 Table, 1994, http://www.unicode.org/Public/MAPPINGS/OBSOLETE/EASTASIA/JIS/JIS0201.TXT.
[JISX0208] The Unicode Consortium., JIS X 0208 (1990) to Unicode, 1994, http://www.unicode.org/Public/MAPPINGS/OBSOLETE/EASTASIA/JIS/JIS0208.TXT.
[UAX11] Asmus Freytag, East Asian Width, Unicode Standard Annex #11, http://www.unicode.org/reports/tr11/tr1119.html, 2009.
The OpenDocument specification defines conformance for formula expressions and evaluators. For evaluators, there are three groups of features that an evaluator may support. This chapter defines the basic requirements for the individual conformance targets.
An OpenDocument formula expression shall adhere to the expression syntax defined in chapter 4. It may use subsets or supersets of OpenFormula.
An OpenDocument Formula Evaluator is a program that can parse and recalculate OpenDocument formula expressions, and that meets the following additional requirements:
A)It may implement subsets or supersets of this specification.
B)It shall conform to one of: (C16) OpenDocument Formula Small Group Evaluator, (C17) OpenDocument Formula Medium Group Evaluator or (C18) OpenDocument Formula Large Group Evaluator
C)It may implement additional functions beyond those defined in this specification. It may further implement additional formula syntax, additional operations, additional optional parameters for functions, or may consider function parameters to be optional when they are required by this specification.
D)Applications should clearly document their extensions in their user documentation, both online and paper, in a manner so users would be likely to be aware when they are using a nonstandard extension.
Note 1: An expression may reference a nonstandard function by name, or depend on implementationdefined behavior, or on semantics not guaranteed by this specification. Reference to or dependence upon functions or behavior not defined by this standard may impair the interoperability of the resulting expression(s).
Note 2: This specification defines formulas in terms of a canonical text representation used for exchange. If formulas are contained in XML attributes some characters shall be escaped as required by the XML specification (e.g., the character & shall be escaped in XML attributes using notations such as &). All string and character literals references by this specification are in the value space defined by [UNICODE] thus, “A” is U+0041, “Z” is U+005A, and the range of characters “AZ” is the range U+0041 through U+005A inclusive.
An OpenDocument Formula Small Group Evaluator is an OpenDocument Formula Evaluator that meets the following additional requirements:
A)It shall implement at least the limits defined in the “Basic Limits” section.
B)It shall implement the syntax defined in these sections on syntax: Criteria; Basic Expressions; Constant Numbers; Constant Strings; Operators; Functions and Function Parameters; Nonstandard Function Names; References; Simple Named Expressions; Errors; Whitespace.
C)It shall implement all implicit conversions for the types it implements, at least Text, Conversion to Number, Reference, Conversion to Logical, and Error.
D)It shall implement the following operators (which are all the operators except reference union (~)): Infix Operator Ordered Comparison ("<", "<=", ">", ">="); Infix Operator "&”; Infix Operator "+”; Infix Operator "”; Infix Operator "*”; Infix Operator "/”; Infix Operator "^”; Infix Operator "=”; Infix Operator "<>”; Postfix Operator “%”; Prefix Operator “+”; Prefix Operator “”; Infix Operator Reference Intersection ("!"); Infix Operator Range (":").
E)It shall implement at least the following functions as defined in this specification: ABS 6.16.2 ; ACOS 6.16.3 ; AND 6.15.2 ; ASIN 6.16.7 ; ATAN 6.16.9 ; ATAN2 6.16.10 ; AVERAGE 6.18.3 ; AVERAGEIF 6.18.5 ; CHOOSE 6.14.3 ; COLUMNS 6.13.5 ; COS 6.16.19 ; COUNT 6.13.6 ; COUNTA 6.13.7 ; COUNTBLANK 6.13.8 ; COUNTIF 6.13.9 ; DATE 6.10.2 ; DAVERAGE 6.9.2 ; DAY 6.10.5 ; DCOUNT 6.9.3 ; DCOUNTA 6.9.4 ; DDB 6.12.14 ; DEGREES 6.16.25 ; DGET 6.9.5 ; DMAX 6.9.6 ; DMIN 6.9.7 ; DPRODUCT 6.9.8 ; DSTDEV 6.9.9 ; DSTDEVP 6.9.10 ; DSUM 6.9.11 ; DVAR 6.9.12 ; DVARP 6.9.13 ; EVEN 6.16.30 ; EXACT 6.20.8 ; EXP 6.16.31 ; FACT 6.16.32 ; FALSE 6.15.3 ; FIND 6.20.9 ; FV 6.12.20 ; HLOOKUP 6.14.5 ; HOUR 6.10.10 ; IF 6.15.4 ; INDEX 6.14.6 ; INT 6.17.2 ; IRR 6.12.24 ; ISBLANK 6.13.14 ; ISERR 6.13.15 ; ISERROR 6.13.16 ; ISLOGICAL 6.13.19 ; ISNA 6.13.20 ; ISNONTEXT 6.13.21 ; ISNUMBER 6.13.22 ; ISTEXT 6.13.25 ; LEFT 6.20.12 ; LEN 6.20.13 ; LN 6.16.39 ; LOG 6.16.40 ; LOG10 6.16.41 ; LOWER 6.20.14 ; MATCH 6.14.9 ; MAX 6.18.45 ; MID 6.20.15 ; MIN 6.18.48 ; MINUTE 6.10.12 ; MOD 6.16.42 ; MONTH 6.10.13 ; N 6.13.26 ; NA 6.13.27 ; NOT 6.15.7 ; NOW 6.10.15 ; NPER 6.12.29 ; NPV 6.12.30 ; ODD 6.16.44 ; OR 6.15.8 ; PI 6.16.45 ; PMT 6.12.36 ; POWER 6.16.46 ; PRODUCT 6.16.47 ; PROPER 6.20.16 ; PV 6.12.41 ; RADIANS 6.16.49 ; RATE 6.12.42 ; REPLACE 6.20.17 ; REPT 6.20.18 ; RIGHT 6.20.19 ; ROUND 6.17.5 ; ROWS 6.13.30 ; SECOND 6.10.16 ; SIN 6.16.55 ; SLN 6.12.45 ; SQRT 6.16.58 ; STDEV 6.18.72 ; STDEVP 6.18.74 ; SUBSTITUTE 6.20.21 ; SUM 6.16.61 ; SUMIF 6.16.62 ; SYD 6.12.46 ; T 6.20.22 ; TAN 6.16.69 ; TIME 6.10.17 ; TODAY 6.10.19 ; TRIM 6.20.24 ; TRUE 6.15.9 ; TRUNC 6.17.8 ; UPPER 6.20.27 ; VALUE 6.13.34 ; VAR 6.18.82 ; VARP 6.18.84 ; VLOOKUP 6.14.12 ; WEEKDAY 6.10.20 ; YEAR 6.10.23
F)It need not evaluate references that contain more than one area.
G)It need not implement inline arrays, complex numbers, and the reference union operator.
Note: This specification does not mandate a user interface for international characters, so a resourceconstrained application may choose to not show the traditional glyph (e.g., it may show the [UNICODE] numeric code instead).
An OpenDocument Formula Medium Group Evaluator is an OpenDocument Small Group Formula Evaluator that meets the following additional requirements:
A)It shall implement the following functions as defined in this specification: ACCRINT 6.12.2 ; ACCRINTM 6.12.3 ; ACOSH 6.16.4 ; ACOT 6.16.5 ; ACOTH 6.16.6 ; ADDRESS 6.14.2 ; ASINH 6.16.8 ; ATANH 6.16.11 ; AVEDEV 6.18.2 ; BESSELI 6.16.12 ; BESSELJ 6.16.13 ; BESSELK 6.16.14 ; BESSELY 6.16.15 ; BETADIST 6.18.7 ; BETAINV 6.18.8 ; BINOMDIST 6.18.10 ; CEILING 6.17.1 ; CHAR 6.20.3 ; CLEAN 6.20.4 ; CODE 6.20.5 ; COLUMN 6.13.4 ; COMBIN 6.16.16 ; CONCATENATE 6.20.6 ; CONFIDENCE 6.18.16 ; CONVERT 6.16.18 ; CORREL 6.18.17 ; COSH 6.16.20 ; COT 6.16.21 ; COTH 6.16.22 ; COUPDAYBS 6.12.5 ; COUPDAYS 6.12.6 ; COUPDAYSNC 6.12.7 ; COUPNCD 6.12.7 ; COUPNUM 6.12.9 ; COUPPCD 6.12.10 ; COVAR 6.18.18 ; CRITBINOM 6.18.19 ; CUMIPMT 6.12.11 ; CUMPRINC 6.12.12 ; DATEVALUE 6.10.4 ; DAYS360 6.10.7 ; DB 6.12.13 ; DEVSQ 6.18.20 ; DISC 6.12.15 ; DOLLARDE 6.12.16 ; DOLLARFR 6.12.17 ; DURATION 6.12.18 ; EFFECT 6.12.19 ; EOMONTH 6.10.9 ; ERF 6.16.27 ; ERFC 6.16.28 ; EXPONDIST 6.18.21 ; FISHER 6.18.26 ; FISHERINV 6.18.27 ; FIXED 6.20.10 ; FLOOR 6.17.3 ; FORECAST 6.18.28 ; FTEST 6.18.30 ; GAMMADIST 6.18.31 ; GAMMAINV 6.18.32 ; GAMMALN 6.16.35 ; GCD 6.16.36 ; GEOMEAN 6.18.34 ; HARMEAN 6.18.36 ; HYPGEOMDIST 6.18.37 ; INTERCEPT 6.18.38 ; INTRATE 6.12.22 ; ISEVEN 6.13.17 ; ISODD 6.13.23 ; ISOWEEKNUM 6.10.11 ; KURT 6.18.39 ; LARGE 6.18.40 ; LCM 6.16.38 ; LEGACY.CHIDIST 6.18.11 ; LEGACY.CHIINV 6.18.13 ; LEGACY.CHITEST 6.18.15 ; LEGACY.FDIST 6.18.23 ; LEGACY.FINV 6.18.25 ; LEGACY.NORMSDIST 6.18.54 ; LEGACY.NORMSINV 6.18.55 ; LEGACY.TDIST 6.18.77 ; LINEST 6.18.41 ; LOGEST 6.18.42 ; LOGINV 6.18.43 ; LOGNORMDIST 6.18.44 ; LOOKUP 6.14.8 ; MDURATION 6.12.26 ; MEDIAN 6.18.47 ; MINVERSE 6.5.3 ; MIRR 6.12.27 ; MMULT 6.5.4 ; MODE 6.18.50 ; MROUND 6.17.4 ; MULTINOMIAL 6.16.43 ; NEGBINOMDIST 6.18.51 ; NETWORKDAYS 6.10.14 ; NOMINAL 6.12.28 ; ODDFPRICE 6.12.31 ; ODDFYIELD 6.12.32 ; ODDLPRICE 6.12.33 ; ODDLYIELD 6.12.34 ; OFFSET 6.14.11 ; PEARSON 6.18.56 ; PERCENTILE 6.18.57 ; PERCENTRANK 6.18.58 ; PERMUT 6.18.59 ; POISSON 6.18.62 ; PRICE 6.12.38 ; PRICEMAT 6.12.40 ; PROB 6.18.63 ; QUARTILE 6.18.64 ; QUOTIENT 6.16.48 ; RAND 6.16.50 ; RANDBETWEEN 6.16.51 ; RANK 6.18.65 ; RECEIVED 6.12.43 ; ROMAN 6.19.17 ; ROUNDDOWN 6.17.6 ; ROUNDUP 6.17.7 ; ROW 6.13.29 ; RSQ 6.18.66 ; SERIESSUM 6.16.53 ; SIGN 6.16.54 ; SINH 6.16.56 ; SKEW 6.18.67 ; SKEWP 6.18.68 ; SLOPE 6.18.69 ; SMALL 6.18.70 ; SQRTPI 6.16.59 ; STANDARDIZE 6.18.71 ; STDEVA 6.18.73 ; STDEVPA 6.18.75 ; STEYX 6.18.76 ; SUBTOTAL 6.16.60 ; SUMPRODUCT 6.16.64 ; SUMSQ 6.16.65 ; SUMX2MY2 6.16.66 ; SUMX2PY2 6.16.67 ; SUMXMY2 6.16.68 ; TANH 6.16.70 ; TBILLEQ 6.12.47 ; TBILLPRICE 6.12.48 ; TBILLYIELD 6.12.49 ; TIMEVALUE 6.10.18 ; TINV 6.18.78 ; TRANSPOSE 6.5.6 ; TREND 6.18.79 ; TRIMMEAN 6.18.80 ; TTEST 6.18.81 ; TYPE 6.13.33 ; VARA 6.18.83 ; VDB 6.12.50 ; WEEKNUM 6.10.21 ; WEIBULL 6.18.86 ; WORKDAY 6.10.22 ; XIRR 6.12.51 ; XNPV 6.12.52 ; YEARFRAC 6.10.24 ; YIELD 6.12.53 ; YIELDDISC 6.12.54 ; YIELDMAT 6.12.55 ; ZTEST 6.18.87
B)It shall implement the Infix Operator Reference Union ("~") 6.4.13
C)It shall evaluate references with more than one area.
An OpenDocument Formula Large Group Evaluator is an OpenDocument Medium Group Formula Evaluator that meets the following additional requirements:
A)It shall implement the syntax defined in these sections on syntax: Inline Arrays; Automatic Intersection; External Named Expressions.
B)It shall implement the complex number type as discussed in the section on Complex Number, array formulas, and Sheetlocal Named Expressions.
It shall implement the following functions as defined in this specification: AMORLINC 6.12.4 ; ARABIC 6.19.2 ; AREAS 6.13.2 ; ASC 6.20.2 ; AVERAGEA 6.18.4 ; AVERAGEIFS 6.18.6 ; BASE 6.19.3 ; BIN2DEC 6.19.4 ; BIN2HEX 6.19.5 ; BIN2OCT 6.19.6 ; BINOM.DIST.RANGE 6.18.9 ; BITAND 6.6.2 ; BITLSHIFT 6.6.3 ; BITOR 6.6.4 ; BITRSHIFT 6.6.5 ; BITXOR 6.6.6 ; CHISQDIST 6.18.12 ; CHISQINV 6.18.14 ; COMBINA 6.16.17 ; COMPLEX 6.8.2 ; COUNTIFS 6.13.10 ; CSC 6.16.23 ; 6.16.23CSCH 6.16.24 ; DATEDIF 6.10.3 ; DAYS 6.10.6 ; DDE 6.11.2 ; DEC2BIN 6.19.7 ; DEC2HEX 6.19.8 ; DEC2OCT 6.19.9 ; DECIMAL 6.19.10 ; DELTA 6.16.26 ; EDATE 6.10.8 ; ERROR.TYPE 6.13.11; EUROCONVERT 6.16.29 ; FACTDOUBLE 6.16.33 ; FDIST 6.18.22 ; FINDB 6.7.2 ; FINV 6.18.24 ; FORMULA 6.13.12 ; FREQUENCY 6.18.29 ; FVSCHEDULE 6.12.21 ; GAMMA 6.16.34 ; GAUSS 6.18.33 ; GESTEP 6.16.37 ; GETPIVOTDATA 6.14.4 ; GROWTH 6.18.35 ; HEX2BIN 6.19.11 ; HEX2DEC 6.19.12 ; HEX2OCT 6.19.13 ; HYPERLINK 6.11.3 ; IFERROR 6.15.5 ; IFNA 6.15.6 ; IMABS 6.8.3 ; IMAGINARY 6.8.4 ; IMARGUMENT 6.8.5 ; IMCONJUGATE 6.8.6 ; IMCOS 6.8.7 ; IMCOT 6.8.9 ; IMCSC 6.8.10 ; IMCSCH 6.8.11 ; IMDIV 6.8.12 ; IMEXP 6.8.13 ; IMLN 6.8.14 ; IMLOG10 6.8.15 ; IMLOG2 6.8.16 ; IMPOWER 6.8.17 ; IMPRODUCT 6.8.18 ; IMREAL 6.8.19 ; IMSEC 6.8.22 ; IMSECH 6.8.23 ; IMSIN 6.8.20 ; IMSQRT 6.8.24 ; IMSUB 6.8.25 ; IMSUM 6.8.26 ; IMTAN 6.8.27; INDIRECT 6.14.7 ; INFO 6.13.13 ; IPMT 6.12.23 ; ISFORMULA 6.13.18 ; ISPMT 6.12.25 ; ISREF 6.13.24 ; JIS 6.20.11 ; LEFTB 6.7.3 ; LENB 6.7.4 ; MAXA 6.18.46 ; MDETERM 6.5.2 ; MULTIPLE.OPERATIONS 6.14.10 ; MUNIT 6.5.5 ; MIDB 6.7.5 ; MINA 6.18.49 ; NORMDIST 6.18.52 ; NORMINV 6.18.53 ; NUMBERVALUE 6.13.28 ; OCT2BIN 6.19.14 ; OCT2DEC 6.19.15 ; OCT2HEX 6.19.16 ; PDURATION 6.12.35 ; PERMUTATIONA 6.18.60 ; PHI 6.18.61 ; PPMT 6.12.37 ; PRICEDISC 6.12.39 ; REPLACEB 6.7.6 ; RIGHTB 6.7.7 ; RRI 6.12.44 ; SEARCH 6.20.20 ; SEARCHB 6.7.8 ; SEC 6.16.52 ; SECH 6.16.57 ; SHEET 6.13.31 ; SHEETS 6.13.32 ; SUMIFS 6.16.63 ; TEXT 6.20.23 ; UNICHAR 6.20.25 ; UNICODE 6.20.26 ; VARPA 6.18.85 ; XOR 6.15.10
Note: The following functions are documented by this specification, but not included even in the Large group:CELL 6.13.3 ; DOLLAR 6.20.7
Applications should document all implementationdefined and variances from this standard in a manner that the application users can obtain the information.
In a few cases a specific approach is required (e.g., string indexes begin at one), which may be different than the user interface of some implementations.
In practice, for nearly all documents the differences are irrelevant. The primary variances and differences from OpenFormula and some existing applications are:
●Some conversions between types are not required to be automatic. In particular, applications may, but need not, perform automatic conversion of text in a cell when it is to be used as a number (see Auto Text to Number).
●There need not be a distinguishable Logical type. Applications may have a Logical type distinct from Number (see Distinct Logical), but Logical values may also be represented by the Number type using the values 1 (True) and 0 (False). This means that functions that take number sequences (such as SUM) may but need not include true and false values in the sequence.
●Applications vary on the set of Errors they support. In this specification. The only distinguished Error is #N/A; all other errors are simply errors, allowing applications to choose the Error set that best meets their needs.
●In this specification, string index positions start from 1. Users of applications with string index positions starting from 0 shall add and subtract 1 on import/export of this format, as appropriate.
●Database criteria match patterns (such as the pattern matching language for text) have historically varied: Some support glob syntax (e.g., a*b is a, followed by 0 or more characters, followed by b), while others support traditional regular expression syntax (e.g., a*b is zero or more a’s, followed by b). This specification supports both pattern languages.
Note: Interoperability is improved by the use of the DATE and TIME functions or the textual [ISO8601] date representation because dates in that format do not rely upon epoch or localespecific settings.
In an OpenDocument file, calculation settings impact formula recalculation, which can be the same or different from a particular application's defaults. These include whether or not text comparisons are casesensitive, or if search criteria shall apply to the whole cell.
This section describes the basic formula processing model: how expressions are calculated, when recalculation occurs, and limits on formulas.
OpenFormula defines rules for the evaluation of expressions as well as the functions and operators that appear in expressions.
Expressions in OpenFormula shall be evaluated by application of the following rules:
1)If an expression consists of a constant Number (5.3), a constant String (5.4), a Reference (5.8), constant Error (per section 5.12), the value of that type is returned.
2)If an expression consists of one or more operations, apply the operators in order of precedence and associativity as defined by Table 1 in 5.5 (Operators). Precedence of operators may be altered by the use of "(" (LEFT PARENTHESES, U+0028) and ")" (RIGHT PARENTHESES, U+0029) to group operators. Evaluate the operator as described in Operator and Function Evaluation, 3.2.3.
3)If an expression consists of a function call (5.6, 5.7), evaluate the function as described in Operator and Function Evaluation, 3.2.3.
4)If an expression consists of a named expression (5.11), the result of evaluating the named expression is returned.
5)If an expression consists of a QuotedLabel (5.10), AutomaticIntersection (5.10.6), or Array (5.13), its value is returned. Expression Syntax 5
Once evaluation has completed:
1)If the result is a Reference and a single nonreference value is needed, it is converted to the referenced value, using the rules of NonScalar Evaluation, 3.3, 1.2.
2)If the result an Array, for the display area, apply the rules of NonScalar Evaluation, 3.3, 1.1.
Operators and functions in OpenFormula shall be evaluated according to their definitions by applying the following rules:
1)The value of all expression arguments are computed. Exceptions to computation of all arguments are noted in a function's specification.
Note: The practice of computing all argument expressions is known as "eager" evaluation. The IF function is an example of a function that does not require computation of all arguments.
2)If an argument expression evaluates to Error, calculation of the operator or function may shortcircuit and return the Error if the function does not suppress error propagation as noted in the function's specification.
3)If an operator or function is passed a value of incorrect type, call the appropriate implicit conversion function to convert the value to the correct type. If conversion is not possible, generate an Error.
4)The function or operation is called with its argument expressions' results, and the result of the function or operation is the evaluation of the expression.
Nonscalar values passed as arguments to functions are evaluated by intersection or iteration.
1)Evaluation as an implicit intersection of the argument with the expression's evaluation position.
1.1)Inline Arrays
Element (0;0) of the array is used in place of the array.
Note 1:
=ABS({3;4}) => ABS(3) // row vector
=ABS({34}) => ABS(3) // column vector
=ABS({3;46;8}) => ABS(3) // matrix
={1;2;34;5;6} => 1 // simple display
1.2)References
1.2.1)If the target reference is a rowvector (Nx1) use the value at the intersection of the evaluation position's column and the reference's row.
Note 2:
in cell B2 : =ABS(A1:C1) => ABS(B1)
If there is no intersection the result is #VALUE!
Note 3: in cell D4 : =ABS(A1:C1) => #VALUE!
1.2.2)If the target reference is a columnvector (1xM) the value at the intersection of the evaluation position's row and the reference's column.
Note 4:
in cell B2 : =ABS(A1:A3) => ABS(A2)
in cell D4 : =ABS(A1:A3) => #VALUE!
2)Matrix evaluation.
If an expression is being evaluated in a cell flagged as a being part of a 'Matrix' (OpenDocument 8.1.3 table:numbermatrixcolumnsspanned):
2.1)The portion of a nonscalar result to be displayed need not be coextensive with a specified display area. The portion of the nonscalar result to be displayed is determined by:
2.1.1)If the position to be displayed exists in the result, display that position.
2.1.2)If the nonscalar result is 1 column wide, subsequent columns in the display area display the value in the first column. This applies to
 scalars '3'
 singletons '{3}'
 column vectors '{123}'
2.1.3)If the nonscalar result is 1 row high, subsequent rows in the display area use the value of the first row. This applies to
 scalars '3'
 singletons '{3}'
 row vectors '{1;2;3}'
2.1.4)If none of the other rules apply #N/A
Note 5:
in matrix A1:B3 with ={1;23;45;6} : cell B2 contains 4. [Rule 2.1.1]
in matrix A1:B3 with ={135} : cell B2 contains 3. [Rule 2.1.1 for row, and Rule 2.1.2 column]
in matrix A1:B3 with ={2;4} : cell B2 contains 4. [Rule 2.1.3 for row, and Rule 2.1.1 column]
in matrix A1:C4 with ={1;23;45;6} : cell C1,A4 contain #N/A. [Rule 2.1.4]
Note 6: if a value is not requested it is not displayed
in matrix A1:B2 with ={1;23;45;6} : the value '6' is not displayed because B3 is not part of the display matrix.
2.2)Calculations with nonscalar inputs are a generalization of (2.1).
When evaluating a formula in 'matrix' mode, and a nonscalar value is passed to a function argument that expects a scalar, the function is evaluated multiple times, iterating over the nonscalar input(s) and putting the function result into a matrix at the position corresponding to the input. Unary/Binary operators, other than range and union, follow the rules for scalar functions when passed nonscalar values.
Inline arrays and references are interchangeable.
2.2.1)Functions returning arrays are not eligible for implicit iteration. When evaluated in 'matrix' mode the {0;0}th element is used.
Note 7:
e.g. =SUM(INDIRECT({"A1";"A2")) would produce the value in A1 when evaluated in array mode.
2.2.2)The result matrix is rectangular, sized with the maximum number of rows and columns from all nonscalar arguments.
Note 8:
={1;2}+{3;4;5} => {4;6;#N/A}
={1}+{1;2} => {2;3}
2.2.3)The result matrix is populated by extracting the corresponding value from each of the nonscalar arguments based on the following rules, and evaluating the function with that set of arguments.
2.2.3.1)If the argument data is a singleton array or a scalar the value is repeated for each evaluation.
Note 9:
= 1 + {1;2;34;5;6} => {2;3;45;6;7}
= {1} + {1;2;34;5;6} => {2;3;45;6;7}
2.2.3.2)If the argument data is 1 column wide the value in the corresponding row is used to evaluate all columns in the result matrix.
Note 10:
= {12} + {10;2030;40} => {11;2132;42}
2.2.3.3)If the argument data is 1 row height the value in the corresponding column is used to evaluate all rows in the result matrix.
Note 11:
= {1;2} + {10;2030;40} => {11;2231;42}
2.2.3.4)If one argument data is 1 column wide and another argument data is 1 row height the value of the corresponding row respectively column is used to evaluate all elements in the result matrix.
Note 12:
={1;2} + {1020} => {11;1221;22}
2.2.3.5)If an argument is a 2d matrix the argument value in the position corresponding to the current output position is used if it is within range of the supplied argument, otherwise #N/A is used in the calculation.
Note 13:
=MID("abcd";{1;2};{1;2;3}) => {"a";"bc";#VALUE!}
A Formula Evaluator operates in an execution environment (a "host"). The behavior of the Formula Evaluator is parametrized by hostdefined properties and functions.
The following properties are hostdefined:
1)HOSTCASESENSITIVE: if true, text comparisons are casesensitive. This influences the operators =, <>, <, <=, >, and >=, as well as database query functions that use them. Note that the EXACT function is always casesensitive, regardless of this calculation setting.
2)HOSTPRECISIONASSHOWN: If true, calculations are performed using rounded values of those displayed; otherwise, calculations are performed using the precision of the underlying numeric representation.
Note: This does not impose a particular numeric model. Since implementations may use binary representations, this rounding may be inexact for decimal value.
3)HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL If true, the specified search criteria shall apply to the entire cell contents if it is a text match using = or <>; if not, only a subpart of the cell content needs to match the text.
4)HOSTAUTOMATICFINDLABELS: if true, row and column labels are automatically found.
5)HOSTUSEREGULAREXPRESSIONS: If true, regular expressions are used for character string comparisons and when searching.
6)HOSTUSEWILDCARDS: If true, wildcards question mark '?' and asterisk '*' are used for character string comparisons and when searching. Wildcards may be escaped with a tilde '~' character.
7)HOSTNULLYEAR: This defines how to convert a twodigit year into a fourdigit year. All twodigit year values are interpreted as a year that equals or follows this year.
8)HOSTNULLDATE: Defines the beginning of the epoch; a numeric date of 0 equals this date.
9)HOSTLOCALE: The locale to be used for localedependent operations, such as conversion of text to dates, or text to numbers.
10) HOSTITERATIONSTATUS: If enabled, iterative calculations of cyclic references are performed.
11) HOSTITERATIONMAXIMUMDIFFERENCE: If iterative calculations of cyclic references are enabled, the maximum absolute difference between calculation steps that all involved formula cells must yield for the iteration to end and yield a result.
12) HOSTITERATIONSTEPS: If iterative calculations of cyclic references are enabled, the maximum number of steps iterations are performed if the results are not within HOSTITERATIONMAXIMUMDIFFERENCE.
The function HOSTREFERENCERESOLVER(Reference) is implementation defined. This function takes as input a Unicode string containing a Reference according to section 4.8 and returns a resolved value.
Implementations of OpenFormula typically recalculate formulas when its information is needed. Typical implementations will note what values a formula depends on, and when those dependent values are changed and the formula's results are displayed, it will reexecute the formulas that depend on them to produce the new results (choosing the formulas in the right order based on their dependencies). Implementations may recalculate when a value changes (this is termed automatic recalculation) or on user command (this is termed manual recalculation).
Some functions' dependencies are difficult to determine and/or should be recalculated more frequently. These include functions that return today's date or time, random number generator functions (such as RAND 6.16.50), or ones that indirectly determine the cells to act on. Many implementations always recalculate formulas including such functions whenever a recalculation occurs. Functions that are always recalculated whenever a recalculation occurs are termed volatile functions. Functions that are often volatile functions include CELL 6.13.3, HYPERLINK 6.11.3, INDIRECT 6.14.7, INFO 6.13.13, NOW 6.10.15, OFFSET 6.14.11, RAND 6.16.50 and TODAY 6.10.19. Functions that depend on the cell position of the formula they are contained in or the position of a cell they reference need to be recalculated whenever that cell is moved, such functions are COLUMN 6.13.4, ROW 6.13.29 and SHEET 6.13.31. In addition, formulas may indicate that they should always be recalculated during a recalculation process by including a forced recalculation marker, as described in the syntax below.
This specification does not, by itself, specify a numerical implementation model, though it does imply some minimal levels of accuracy for most functions. For example, an application cannot say that it implements the infix operator “/” as specified in this document if it implements integeronly arithmetic.
Evaluators which claim to support “basic limits” shall support at least the following limits:
1.formulas up to at least 1024 characters long, as measured when in OpenDocument interchange format not counting the square brackets around cell addresses, or the “.” in a cell address when the sheet name is omitted.
2.at least 30 parameters per function when the function prototype permits a list of parameters.
3.permit strings of ASCII characters of up to 32,767 (2^151) characters.
4.support at least 7 nesting levels of functions.
All values defined by OpenFormula have a type. OpenFormula defines Text, Number, Complex Number, Logical, Error, Reference, ReferenceList and Array types.
A Text value (also called a string value) is a Character string" per [CharModel].
A text value of length zero is termed the empty string.
Index positions in a text value begin at 1.
Whether or not Unicode Normalization [UTR15] is performed on formulas, formula results or user inputs is implementationdefined. Some functions defined in this Part are labeled as "normalizationsensitive", meaning that the results of the formula evaluation may differ depending on whether normalization occurs, and which normalization form is used. Mixing operands of different normalization forms in the same calculation is undefined.
A number is a numeric value.
Numbers shall be able to represent fractional values (they shall not be limited to only integers). Evaluators may implement Number with a fixed or with a variable bit length. A cell with a constant numeric value has the Number type.
Implementations typically support many subtypes of Number, including Date, Time, DateTime, Percentage, fixedpoint arithmetic, and arithmetic supporting arbitrarily long integers, and determine the display format from this. All such Number subtypes shall yield True for the ISNUMBER 6.13.22 function. This specification does not require that specific subtypes be distinguishable from each other, or that the subtype be tracked, but in practice most implementations do such tracking because requiring users to manually format every cell appropriately becomes tedious very quickly. Automatically determining the most likely subtype is especially important for a good user interface when generating OpenDocument format, since some subtypes (such as date, time, and currency) are stored in a different manner depending on their subtype. Thus, this specification identifies some common subtypes and identifies those subtypes where relevant in some function definitions, as an aid to implementing good user interfaces. Many applications vary in the subtype produced when combining subtypes (e.g., what is the result when percentages are multiplied together), so unless otherwise noted these are unspecified. Typical implementations try to heuristically determine the "right" format for a cell when a formula is first created, based on the operations in the formula. Users can then override this format, so as a result the heuristics are not important for data exchange (and thus outside the scope of this specification).
All Number subtypes shall yield True for the ISNUMBER function.
Time is a subtype of Number.
Time is represented as a fraction of a day.
Date is a subtype of Number.
Date is represented by an integer value.
A serial date is the expression of a date as the number of days elapsed from a start date called the epoch.
Evaluators shall support all dates from 19040101 through 99991231 (inclusive) in calculations, should support dates from 18991230 through 99991231 (inclusive) and may support a wider date range.
Note 1: Using expressions that assume serial numbers are based on a particular epoch may cause interoperability issues.
Evaluators shall support positive serial numbers. Evaluators may support negative serial numbers to represent dates before an epoch.
Note 2: It is implementationdefined if the year 1900 is treated as a leap year.
Note 3: Evaluators that treat 1900 as a nonleap year can use the epoch date 18991230 to compensate for serial numbers that originate from evaluators that treat 1900 as a leap year and use 18991231 as an epoch date.
DateTime is a subtype of Number. It is a Date plus Time.
A percentage is a subtype of Number that may be displayed by multiplying the number by 100 and adding the sign “%” or with other formatting depending upon the number format assigned to the cell where it appears.
A currency is a subtype of Number that may appear with or without a currency symbol or with other formatting depending upon the number format assigned to the cell where it appears.
A Logical value is a subtype of Number where TRUE() returns 1 and FALSE() returns 0.
The implicit conversion operator “Convert to Logical” 6.3.12, when a Number is passed as a condition, 0 is considered False and all other numeric values are considered True.
Note: Logical values can be a distinct type from Number. 4.5
A complex number may, but need not be, represented as a Number or Text. The results of the functions ISNUMBER() and ISTEXT() are implementationdefined when applied to a complex number.
Functions and operators that accept complex numbers shall accept Text values as complex numbers (6.3.10 Conversion to Complex Number, as well as Numbers that are not complex numbers.
Note 1: IMSUM("3i";4) will produce the same result as COMPLEX(4;3).
Note 2: Expression authors should be aware that use of functions that are not defined by OpenFormula as accepting complex numbers as input may impair interoperability.
Equality can be tested using IMSUB to compute the difference, use IMABS to find the absolute difference, and then ensure the absolute difference is smaller than or equal to some nonnegative value (for exact equality, compare for equality with 0).
A Logical value (also called a Boolean value) is a value with one of two values: TRUE() and FALSE().
Note: Logical values can be represented as a subtype of Number. 4.3.7
An Error is one of a set of possible error values. Implementations may have many different error values, but one error value in particular is distinct: #N/A, the result of the NA() function. Users may choose to enter some data values as #N/A, so that this error value propagates to any other formula that uses it, and may test for this using the function ISNA().
Functions and operators that receive one or more error values as an input shall produce one of those input error values as their result, except when the formula or operator is specifically defined to do otherwise.
In an OpenDocument document, if an error value is the result of a cell computation it shall be stored as if it was a string. That is, the office:valuetype of an error value is string; if the computed value is stored, it is stored in the attribute office:stringvalue.
Note: This does not change an Error into a string type (since the Error will be restored on recalculation); this enables applications which cannot recalculate values to display the error information.
An empty cell is neither zero nor the empty string, and an empty cell can be distinguished from cells containing values (including zero and the empty string). An empty cell is not the same as an Error, in particular, it is distinguishable from the Error #N/A (not available).
A cell strip consists of cell positions in the same row and in one or more contiguous columns.
A cell rectangle consists of cell positions in the same cell strips of one or more contiguous rows.
A cell cuboid consists of cell positions in the same cell rectangles of one or more contiguous sheets.
A reference is the smallest cuboid that (1) contains specificallyidentified cell positions and/or specificallyidentified complete columns/rows such that (2) removal of any cell positions either violates condition (1) or does not leave a cuboid.
Cell positions in a cell cuboid/rectangle/strip can resolve to empty cells (section 3.7).
The definitions of specific operations and functions that allow references as operands and parameters stipulate any particular limitations there are on forms of references and how empty cells, when permitted, are interpreted.
A reference list contains 1 or more references, in order. A reference list can be passed as an argument to functions where passing one reference results in an identical computation as an arbitrary sequence of single references occupying the identical cell range.
Note 1: For example, SUM([.A1:.B2]) is identical to SUM([.A1]~[.B2]~[.A2]~[.B1]), but COLUMNS([.A1:.B2]), resulting in 2 columns, is not identical to COLUMNS([.A1]~[.B2]~[.A2]~[.B1]), where iterating over the reference list would result in 4 columns.
A reference list cannot be converted to an array.
Note 2: For example, in array context {ABS([.A1]~[.B2]~[.A2]~[.B1])} is an invalid expression, whereas {ABS([.A1:.B2])} is not.
Passing a reference list where a function does not expect one shall generate an Error. Passing a reference list in array iteration context to a function expecting a scalar value shall generate an Error.
An array is a set of rows each with the same number of columns that contain one or more values. There is a maximum of one value per intersection of row and column. The intersection of a row and column may contain no value.
Many functions require a type or a set of types with special properties, and/or process them specially. For example, a "Database" requires headers that are the field names. These specialized types are called pseudotypes.
A Scalar value is a value that has a single value. A reference to more than one cell is not a scalar (by itself), and shall be converted to one as described below. An array with more than one element is not a scalar. The types Number (including a complex number), Logical, and Text are scalars.
A DateParam is a value that is either a Number (interpreted as a serial number; 4.3.3) or Text; text is automatically converted to a date value. 6.3.15
A TimeParam is a value that is either a Number (interpreted as a serial number; 4.3.2) or Text; text is automatically converted to a time value (fraction of a day). 6.3.16
An integer is a subtype of Number that has no fractional value. An integer X is equal to INT(X). Division of one integer by another integer may produce a noninteger.
TextOrNumber is a value that is either a Number or Text.
A basis is a subtype of Integer that specifies the daycount convention to be used in a calculation.
This standard defines five daycount conventions, corresponding to widely used current and historical accounting conventions. Each of these five bases defines two things:
1.How to calculate the number of days between two dates, date1 and date2.
2.How to calculate the number of days in each year between two dates, date1 and date2.
Historically daycount bases used the naming convention x/y, which indicated that the convention assumed x days per month and y days per year. These names are given for reference purposes.
Date Basis  Historical Name  Day Count  Days in Year 
0  US (NASD) 30/360  Procedure A, 4.11.7.3  Procedure D, 4.11.7.6 
1  Actual/Actual  Procedure B, 4.11.7.4  Procedure E, 4.11.7.7 
2  Actual/360  Procedure B, 4.11.7.4  Procedure D, 4.11.7.6 
3  Actual/365  Procedure B, 4.11.7.4  Procedure F, 4.11.7.8 
4  European 30/360  Procedure C, 4.11.7.5  Procedure D, 4.11.7.6 
4.11.7.2Procedural Notation
The daycount procedures are expressed using notations defined as:
•.day(date) returns the day of the month for the given date value, an integer from 1 to 31
•.month(date) returns the month of a given date value, an integer from 112
•.year(date) returns the year of the given date value
•.truncate(date) truncates any fractional (hours, minutes, seconds) of a date value and returns the whole date portion.
•.Binary comparison operators date1>date2 and date1 == date2
•.isleapyear(year) returns true if year is a leap year, otherwise false.
Note: Some of the day count procedures use intermediate results that contain counterfactual dates, such as February 30th. This is not an error. The above functions work on such dates as well, e.g., day(February 30th) = = 30.
1.truncate(date1), truncate(date2)
2.If date1==date2 return 0
3.If date1> date2, then swap the values of date1 and date2.
4.If day(date1)==31 then subtract 1 day from date1
5.If day(date1)==30 and day(date2)==31 then subtract 1 day from date2
6.If both date1 and date2 are the last day of February, change date2 to the 30th of the month.
7.If date1 is the last day of February, change it to the 30th of the month.
8.Return (year(date2)*360 + month(date2)*30 + day(date2))  (year(date1)*360 + month(date1)*30 + day(date1)).
1.truncate(date1), truncate(date2)
2.If date1> date2, then swap the values of date1 and date2.
3.Return the actual numbers of days between date1 and date2, inclusive of date1, but not inclusive of date2.
1.truncate(date1), truncate(date2)
2.If date1==date2 return 0
3.If date1> date2, then swap the values of date1 and date2.
4.If day(date1)==31 then subtract 1 from date1
5.If day(date2)==31 then subtract 1 from date 2
6.Return (year(date2)*360 + month(date2)*30 + day(date2))  (year(date1)*360 + month(date1)*30 + day(date1)).
1.Return 360
1.Evaluate A: year(date1) != year(date2)
2.Evaluate B: year(date2)!=year(date1)+1
3.Evaluate C: month(date1) < month(date2)
4.Evaluate D: month(date1) == month(date2)
5.Evaluate E: day(date1) < day(date2)
6.Evaluate F: (A and B) or (A and C) or (A and D and E)
7.If F is true then return the average of the number of days in each year between date1 and date2, inclusive.
8.Otherwise, if A and isleapyear(year(date1)) then return 366
9.Otherwise, if a February 29 occurs between date1 and date2 then return 366
10. Otherwise, if date2 is a February 29, then return 366
11. Otherwise return 365
1.Return 365
A criterion is a single cell Reference, Number or Text. It is used in comparisons with cell contents.
A reference to an empty cell is interpreted as the numeric value 0.
A matching expression can be:
●A Number or Logical value. A matching cell content equals the Number or Logical value.
●A value beginning with a comparator (<, <=, =, >, >=, <>). 6.4.9
For =, if the value is empty it matches empty cells. 4.7
For <>, if the value is empty it matches nonempty cells.
For <>, if the value is not empty it matches any cell content except the value, including empty cells.
Note: "=0" does not match empty cells.
For = and <>, if the value is not empty and can not be interpreted as a Number type or one of its subtypes and the hostdefined property HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL is true, comparison is against the entire cell contents, if false, comparison is against any subpart of the field that matches the criteria. For = and <>, if the value is not empty and can not be interpreted as a Number type or one of its subtypes 3.4 applies.
●Other Text value. If the hostdefined property HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL is true, the comparison is against the entire cell contents, if false, comparison is against any subpart of the field that matches the criteria.
A database is a rectangular organized set of data. Any database has a set of one or more fields that determine the structure of the database. A database has a set of zero or more records with data, and each record contains data for every field (though that field may be empty).
Evaluators shall support the use of ranges as databases if they support any database functions. The first row of a range is interpreted as a set of field names.
Note: Field names of type Text and unique without regard to case enhance the interoperability of data. It is also a common expectation that rows following the first row of data are data records that correspond to field names in the first row.
A single cell containing text can be used as a database; if it is, it is a database with a single field and no data records.
A field is a value that selects a field in a database; it is also called a field selector. If the field selector is Text, it selects the field in the database with the same name.
Evaluators should match the database field name case insensitive.
If a field selector is a Number, it is a positive integer and used to select the fields. Fields are numbered from left to right beginning with the number 1.
All functions that accept a field parameter shall, when evaluated, return an Error if the selected field does not exist.
A criteria is a rectangular set of values, with at least one column and two rows, that selects matching records from a database. The first row lists fields against which expressions will be matched. 4.11.10 Rows after the first row contain fields with expressions for matching against database records.
For a record to be selected from a database, all of the expressions in a row of criteria shall match.
A reference to an empty cell is interpreted as the numeric value 0.
Some functions accept a sequence, i.e., a value that is to be treated as a sequential series of values. The following are sequences: NumberSequence, NumberSequenceList, DateSequence, LogicalSequence, and ComplexSequence.
When evaluating a function that accepts a sequence, the evaluator shall follow the rules for that sequence as defined in section 6.3. When processing a ReferenceList, the references are processed in order (first, second if any, and so on). In a cuboid, the first sheet is first processed, followed by later sheets (if any) in order. Inside a sheet, it is implementationdefined as to whether the values are processed rowatatime or columnatatime, but it must be one of these two processing orders. If processing rowatatime, the sequence must be produced by processing each row in turn, from smallest to largest column value (e.g., A1, B1, C1). If processing columnatatime, the sequence must be produced by processing each column at a time, from the smallest to the largest row value (e.g., A1, A2, A3).
Any represents a value of any type defined in this standard, including Error values.
The OpenFormula syntax is defined using the BNF notation of the XML specification, chapter 6 [XML1.0]. Each syntax rule is defined using "::=".
Note: Formulas are typically embedded inside an XML document. When this occurs, characters (such as "<", ">", '"', and "&") shall be escaped, as described in section 2.4 of the XML specification [XML1.0]. In particular, the lessthan symbol "<" is typically represented as “<”, the doublequote symbol as “"”, and the ampersand symbol as “&” (alternatively, a numeric character reference can be used).
Formulas may start with a '=' (EQUALS SIGN, U+003D), which if present may be followed by a “forced recalculate” marker '=' (EQUALS SIGN, U+003D), followed by an expression. If the second '=' (EQUALS SIGN, U+003D) is present, this formula is a "forced recalculation" formula. If a formula is marked as a "forced recalculation" formula, then it should be recalculated whenever one of its predecessors it depends on changes.
Expressed in BNF grammar, a formula is specified:
Formula ::= Intro? Expression
Intro ::= '=' ForceRecalc?
ForceRecalc ::= '='
The primary component of a formula is an Expression . Formulas are composed of Expression s, which may in turn be composed from other Expression s.
Expression ::=
Whitespace* (
Number 
String 
Array 
PrefixOp Expression 
Expression PostfixOp 
Expression InfixOp Expression 
'(' Expression ')' 
FunctionName Whitespace* '(' ParameterList ')' 
Reference 
QuotedLabel 
AutomaticIntersection 
NamedExpression 
Error
) Whitespace*
SingleQuoted ::= "'" ([^']  "''")+ "'"
Constant numbers are written using '.' (FULL STOP, U+002E) dot as the decimal separator. Optional "E" or "e" denotes scientific notation. Syntactically, negative numbers are positive numbers with a prefix "" (HYPHENMINUS, U+002D) operator. A constant number is of type Number.
Number ::= StandardNumber 
'.' [09]+ ([eE] [+]? [09]+)?
StandardNumber ::= [09]+ ('.' [09]+)? ([eE] [+]? [09]+)?
Evaluators should be able to read the Number format, which accepts a decimal fraction that starts with decimal point '.' (FULL STOP, U+002E), without a leading zero. Evaluators shall write numbers only using the StandardNumber format, which requires a leading digit, and shall not write numbers with a leading '.' (FULL STOP, U+002E).
Constant strings are surrounded by doublequote characters (QUOTATION MARK, U+0022); a literal doublequote character '"' (QUOTATION MARK, U+0022) as string content is escaped by duplicating it. A constant string is of type Text.
String ::= '"' ([^"#x00]  '""')* '"'
Operators are functions with one or more parameters.
PrefixOp ::= '+'  ''
PostfixOp ::= '%'
InfixOp ::= ArithmeticOp  ComparisonOp  StringOp  ReferenceOp
ArithmeticOp ::= '+'  ''  '*'  '/'  '^'
ComparisonOp ::= '='  '<>'  '<'  '>'  '<='  '>='
StringOp ::= '&'
There are three predefined reference operators: reference intersection , reference concatenation , and range. The result of these operators may be a 3 dimensional range, with frontupperleft and backlowerright corners, or even a list of such ranges in the case of cell concatenation.
ReferenceOp ::= IntersectionOp  ReferenceConcatenationOp  RangeOp
IntersectionOp ::= '!'
ReferenceConcatenationOp ::= '~'
RangeOp ::= ':'
Table 1  Operators defines the associativity and precedence of operators, from hightest to lowest precedence.
Table 1  Operators
Associativity  Operator(s)  Comments 
left  :  Range. 
left  !  Reference intersection ([.A1:.C4]![.B1:.B5] is [.B1:.B4]). Displayed as the space character in some implementations. 
left  ~  Reference union. Displayed as the function parameter separator in some implementations. 
right  +,  Prefix unary operators, e.g., 5 or [.A1]. Note that these have a different precedence than add and subtract. 
left  %  Postfix unary operator % (divide by 100). Note that this is legal with expressions (e.g., [.B1]%). 
left  ^  Power (2 ^ 3 is 8). 
left  *,/  Multiply, divide. 
left  +,  Binary operations add, subtract. Note that unary (prefix) + and  have a different precedence. 
left  &  Binary operation string concatenation. Note that unary (prefix) + and  has a different precedence. Note that "&" shall be escaped when included in an XML document 
left  =, <>, <, <=, >, >=  Comparison operators equal to, not equal to, less than, less than or equal to, greater than, greater than or equal to 
Note 1: Prefix “” has a higher precedence than “^”, that “^” is leftassociative, and that reference intersection has a higher precedence than reference union.
Note 2: Prefix “+” and “–“ are defined to be rightassociative. However, note that typical applications which implement at most the operators defined in this specification (as specified) may implement them as leftassociative, because the calculated results will be identical.
Note 3: Precedence can be overridden by using parentheses, so "=2+3*4" computes to 14 but "=(2+3)*4" computes 20. Implementations should retain "unnecessary" parentheses and white space, since these are added by people to improve readability.
Functions are called by name, followed by parentheses surrounding a list of parameters. Parameters are separated using the semicolon ';' (SEMICOLON, U+003B) character:
FunctionName ::= LetterXML (LetterXML  DigitXML 
'_'  '.'  CombiningCharXML)*
Where LetterXML, DigitXML, and CombiningCharXML are Letter, Digit, and CombiningChar as they are defined in [XML1.0].
Function names are caseinsensitive.
Function calls shall be given a parameter list, though it may be empty. An empty list of parameters is considered a call with 0 parameters, not a call with one parameter that happens to be empty. TRUE() is syntactically a function call with 0 parameters. It is syntactically legitimate to provide empty parameters, though functions need not accept empty parameters unless otherwise noted:
ParameterList ::= /* empty */ 
Parameter (Separator EmptyOrParameter )* 
Separator EmptyOrParameter /* First param empty */
(Separator EmptyOrParameter )*
EmptyOrParameter ::= /* empty */ Whitespace*  Parameter
Parameter ::= Expression
Separator ::= ';'
When writing a document using function(s) not defined in this specification, an evaluator shall include a prefix in such function names to identify the original definer of the function's semantics. When the origin of a function cannot be determined, producers may omit a prefix. Producers may use the prefix to differentiate between different definition types. Evaluators that do not support a function should compute its result as some Error value other than NA().
Note: Examples of implementationdefined functions include extension functions included with an implementation, userdefined functions written by users, and 3rd party functions distributed in libraries.
Note: Examples of such names include COM.MICROSOFT.CUBEMEMBER, ORG.OPENOFFICE.STYLE, ORG.GNUMERIC.RANDRAYLEIGH, and COM.LOTUS.V98.FOO.
Evaluators should avoid defining evaluatorunique functions beginning with a toplevel domain name followed by a period. Evaluators should avoid defining application functions beginning with “NET.”, “COM.”, “ORG.”, or a country code followed by a period.
Evaluators that do not support a function should compute its result as some Error value other than NA().
References refer to a specific cell or set of cells. The syntax for a constant reference:
Reference ::= '[' (Source? RangeAddress)  ReferenceError ']'
RangeAddress ::=
SheetLocatorOrEmpty '.' Column Row (':' '.' Column Row )? 
SheetLocatorOrEmpty '.' Column ':' '.' Column 
SheetLocatorOrEmpty '.' Row ':' '.' Row 
SheetLocator '.' Column Row ':' SheetLocator '.' Column Row 
SheetLocator '.' Column ':' SheetLocator '.' Column 
SheetLocator '.' Row ':' SheetLocator '.' Row
SheetLocatorOrEmpty ::= SheetLocator  /* empty */
SheetLocator ::= SheetName ('.' SubtableCell)*
SheetName ::= QuotedSheetName  '$'? [^\]\. #$']+
QuotedSheetName ::= '$'? SingleQuoted
SubtableCell ::= ( Column Row )  QuotedSheetName
ReferenceError ::= "#REF!"
Column ::= '$'? [AZ]+
Row ::= '$'? [19] [09]*
Source ::= "'" IRI "'" "#"
CellAddress ::= SheetLocatorOrEmpty '.' Column Row /* Not used directly */
References always begin with '[' (LEFT SQUARE BRACKET, U+005B); this disambiguates cell addresses from function names and named expressions. SheetNames include singlequote“'” (APOSTROPHE, U+0027) characters by doubling them and having the entire name surrounded by singlequotes. Column labels shall be in uppercase. The syntax supports wholerow and wholecolumn references. A reference is of type Reference.
A ReferenceError provides information that a formula evaluates to an Error because of a particular reference having been invalidated by actions that occurred after the formula was validly created.
Columns are named by a sequence of one or more uppercase letters AZ (U+0041 through U+005A). Columns are named A, B, C, ... X, Y, Z, AA, AB, AC, ... AY, AZ, BA, BB, BC, ... ZX, ZY, ZZ, AAA, AAB, AAC, AAZ, ABA, ABB, and so on.
If a RangeAddress does not contain a Column element or does not contain a Row element, it specifies a cell rectangle (4.8 Reference). If it contains Row elements, the cell rectangle starts on the first column and ends on the last column the evaluator supports. If it contains Column elements, the cell rectangle starts on the first row and ends on the last row the evaluator supports.
If in a RangeAddress the first part (left of ':' colon) contains a SheetLocator and the second part (right of ':' colon) does not contain a SheetLocator, the second part inherits the SheetLocator from the first part.
If a RangeAddress contains two different SheetLocators, it specifies a cell cuboid (4.8 Reference).
If a RangeAddress contains no SheetLocator, the current sheet local to the position where the expression is evaluated is referred.
A reference with an explicit row or column value beyond the capabilities of an evaluator shall be computed as an Error, and not as a reference.
Note that references can include a single embedded “:” separator. Evaluators should use references with embedded “:” separators inside the [..] markers, instead of the generalpurpose “:” operator, when saving files, and where there is a choice of cells to join, and evaluators should choose the leftmost pair.
The optional Source expresses that the reference is to sheets and/or cells in a different location (possibly in a samedocument fragment) than that for the formula in which the reference occurs. The optional Source is also used for locating Named Expressions (section 5.11).
The IRI portion of Source shall be an IRI reference [RFC3987] conforming to the general syntax IRIreference rule (section 2.2 of [RFC3987]) after each pair of consecutive singlequote characters (APOSTROPHE, U+0027) is replaced by one single singlequote character.
Note: The escaping of singlequotes as paired singlequotes is because the IRI is enclosed in single quote characters of the Source.
Resolution of the [RFC3987] IRI reference is hostdefined behavior. 3.4
A reference list is the result of the Infix Operator Reference Concatenation 6.4.13 '~', the syntax is:
ReferenceList ::= Reference (Whitespace* ReferenceConcatenationOp Whitespace* Reference)*
A reference list can be passed as an argument to functions expecting a reference parameter where passing one reference results in an identical computation as an arbitrary sequence of single references occupying the identical cell range. A reference list cannot be converted to an array.
A quoted label is Text contained in a table as cell content, either literally or as a formula result.
QuotedLabel ::= SingleQuoted
A quoted label identifies a column or a row, depending on the label range in which its text appears.
For a QuotedLabel, first the cells defined in column label ranges (cell ranges of the table:labelcellrangeaddress attribute in the elements <table:labelrange> with attribute table:orientation set to column) are searched for the string content of QuotedLabel (without the quotes). If found, the corresponding column's range of the data cell range of the table:datacellrangeaddress attribute is taken as a reference. If not found, the cells defined in row label ranges (attribute table:orientation set to row) are searched and if found the corresponding row's range of the data cell range is taken. Label ranges of the current formula's sheet take precedence over label ranges of other sheets if a name occurs in both.
For a QuotedLabel where no defined label is found, an automatic lookup is performed on the sheet where the formula cell resides, if that document setting is enabled (HOSTAUTOMATICFINDLABELS value true ).
Matches to the upper left of the formula cell are preferred over other matches, followed by matches with a smaller distance. The following algorithm is used:
Cells on the same sheet as the formula cell are examined columnwise from left to right whether they contain the text of QuotedLabel (without the quotes). If more than one cell match, the distance and direction from the formula cell's position is taken into account. The distance is calculated by Distance= ColumnDifference*ColumnDifference+ RowDifference*Row Difference using an idealized layout of quadratic cells. For the direction, during the run two independent match positions are remembered each time Distance is smaller than a previous Distance: Match2 for positions right of and/or below the formula position (FormulaColumn < MatchColumn  FormulaRow < MatchRow), Match1 for all others (not right of and not below). Match1 also holds the very first match, in case there is only one match or all matches are somewhere below or right of the formula cell. After having found the smallest distances the conditions are:
1.If Match1 has the smallest distance, that match is taken.
2.Else, Match2 (right and/or below) has the smallest or an equal distance:
2.1 A match to the upper left (FormulaColumn >= Match1Column && FormulaRow >= Match1Row) takes precedence over matches to other directions.
2.2 Else, if there is no match to the upper left:
2.2.1 If Match1 is somewhere right of the formula cell (FormulaColumn < Match1Column) it was the first match found in columnwise lookup.
2.2.1.1 If Match2 is above the formula cell (FormulaRow >= Match2Row) it is to the upper right of the formula cell and either nearer than Match1 or Match1 is below. Match2 is taken.
2.2.1.2 Else Match2 is below the formula cell and Match1 is taken.
2.2.2 Else (Match1 not right of the formula cell => two matches below or below and right) the match with the smallest distance is taken.
If the resulting cell is below or above another cell containing Text a row lable is assumed, else a column label is assumed.
Note: Use of automatically looked up column or row labels in expressions impairs interoperability.
For the reference resulting from a single QuotedLabel an implicit intersection is generated if the operator or function where it is used with expects a scalar value. The intersection is generated with the current formula's cell position, thus for a column label an intersection is generated with the formula cell's row, for a row label with the formula cell's column.
When passed as a nonscalar argument (e.g. Array or NumberSequence) to a function, an automatically looked up column or row label (not defined label range) is converted to an automatic range reference that is adjusted each time the formula is interpreted. The range is generated from the column below a column label, or the row right of a row label, constructed by encompassing contiguous nonempty cells. An empty cell interrupts contiguousness, one empty cell directly below a column label cell or right of a row label cell is ignored.
Example:
Table 2  Automatic Range
Row  Data  Expression  Result  Comment 
 =SUM('Label')  3  Empty cell in row 2 is skipped (two empty cells in row 2 and 3 would not and stop), empty cell in row 5 stops the automatic range. 
If any cell content is entered in row 5 the range is regenerated as follows:
Table 3  Automatic Range
Row  Data  Expression  Result  Comment 
 =SUM('Label')  15  Empty cell in row 2 is skipped, empty cell in row 7 stops the automatic range. 
An automatic intersection may be used to identify the intersection of two quoted labels. Note that this is different from the IntersectionOp, which takes two references instead of two labels:
AutomaticIntersection ::= QuotedLabel Whitespace* '!!' Whitespace* QuotedLabel
In an automatic intersection, one of the labels identifies a row, the other a column; they may be in either order. Each QuotedLabel is looked up as defined above under "Lookup of Defined Lables" and "Automatic Lookup of Labels". If two data cell ranges are found, the intersection of the column's data cell range and the row's data cell range is generated. If the intersection result is not exactly one cell, an Error is generated.
A NamedExpression references another expression, possibly in a completely different spreadsheet or any other document type that can be imported into a spreadsheet.
NamedExpression ::= SimpleNamedExpression 
SheetLocalNamedExpression  ExternalNamedExpression
SimpleNamedExpression ::= Identifier 
'$$' (Identifier  SingleQuoted)
SheetLocalNamedExpression ::=
QuotedSheetName '.' SimpleNamedExpression
ExternalNamedExpression ::=
Source (SimpleNamedExpression  SheetLocalNamedExpression)
Evaluators supporting named expressions shall support Simple Named Expressions that are global to all the sheets in a (spreadsheet) document in the current document. This is a named expression without a Source, QuotedSheetName, or SubtableCell. The type of a named expression is the type of the value that the named expression returns.
Named expressions are caseconsistent, meaning that matching is done caseinsensitive and identifiers can not differ ONLY in their case. Evaluators should write identifiers with identical case in all locations.
Evaluators may support Sheetlocal Named Expressions that are local (attached) to individual sheets. In that case, a nonempty QuotedSheetName can be used to reference a sheetspecific named expression. The most specific named expression for a given expression is used. If the QuotedSheetName is empty, the search for the named expression begins with the current sheet, then up through the container(s) of the sheet (the same is true if the QuotedSheetName rule fragment is not included at all). If there is a nonempty QuotedSheetName, search begins with that named sheet, then up through its container(s) for the given name.
Note: There is no syntax for referencing a named expression without first looking at the current sheet's named expressions; where this is a problem, a user can define a blank sheet and reference that sheet as the starting location for finding the named expression.
If a sheetname is not empty, it shall be quoted using “'” (APOSTROPHE, U+0027). While both Source and QuotedSheetName can begin with the singlequote character “'” (APOSTROPHE, U+0027), they are distinguished: after the closing singlequote character, a nonempty source shall have the '#' (NUMBER SIGN, U+0023) character as the next nonwhitespace; a nonempty sheetname shall be followed by the '.' (FULL STOP, U+002E) character as the next nonwhitespace.
Expressions should limit the names of their identifiers to only ([UNICODE]) letters, underscores, and digits, not including patterns that look like cell references or the words True or False.
Identifier ::= ( LetterXML
Evaluators shall support the Error value #N/A. Evaluators may support other Error values. Evaluators may allow entry of errors directly, parse them and recognize them as Errors. Functions shall propagate Errors unless stated otherwise.
Inline Error constants shall have the following syntax:
Error ::= '#' [AZ09]+ ([!?]  ('/' ([AZ]  ([09] [!?]))))
Specific Error values are indicated by an identifier.
Table 4 is a list of constant error names that are used by several existing implementations. Evaluators may implement other constant Error values.
Table 4  Possible Other Constant Error Values
Name  Comments 
#DIV/0!  Attempt to divide by zero, including division by an empty cell. ERROR.TYPE of 2 
#NAME?  Unrecognized/deleted name. ERROR.TYPE of 5. 
#N/A  Not available. ISNA() applied to this value will return True. Lookup functions which failed, and NA(), return this value. ERROR.TYPE of 7. 
#NULL!  Intersection of ranges produced zero cells. ERROR.TYPE of 1. 
#NUM!  Failed to meet domain constraints (e.g., input was too large or too small). ERROR.TYPE of 6. 
#REF!  Reference to invalid cell (e.g., beyond the application’s abilities). ERROR.TYPE of 4. 
#VALUE!  Parameter is wrong type. ERROR.TYPE of 3. 
An unknown constant Error value shall be mapped into an Error value supported by the evaluator when read (e.g., the application's equivalent of #NAME?), though an evaluator may warn the user if this has or will take place. It is desirable to preserve the original specific Error name when writing an Error constant back out, where possible, but evaluators may write a different Error value for a formula than they did when reading it for Errors other than #N/A. Whitespace shall not be included in an Error name.
Evaluators should use a humancomprehensible name, not a numeric id, for constant Error values they write.
Inline arrays are enclosed with curly braces. Inside, they contain one or more rows, with each row separated by a row separator:
Array ::= '{' MatrixRow ( RowSeparator MatrixRow )* '}'
MatrixRow ::= Expression ( ';' Expression )*
RowSeparator ::= ''
Evaluators that support inline arrays shall accept a matrix with one or more rows, each with one or more columns, with the same number of columns in each row, with constant values for each expression. Evaluators that do not support inline arrays, or cannot support a particular use permitted by this syntax, should compute an Error value for such arrays. An inline array is of type Array.
Note: Expression authors should be aware that use of Expression other than constant Number or constant String may impair interoperability.
Whitespace ::= #x20  #x09  #x0a  #x0d
For calculation purposes, whitespace is ignored unless it is inside the contents of string constants or text surrounded by single quotes. Evaluators shall ignore any whitespace characters before and/or after any operators, constant numbers, constant strings, constant errors, inline arrays, parentheses used for controlling precedence, and the closing parenthesis of a function call. Whitespace shall be ignored following the initial equal sign(s). Whitespace shall be ignored just before a function name, but whitespace shall not separate a function name from its initial opening parentheses. Whitespace shall not be used in the interior of a terminating grammar rule (a rule that references no other rule other than character sets, internally or externallydefined), unless specifically permitted by the terminating grammar rule, since these rules define the lexical properties of a component. Evaluators shall not write formulas with whitespace embedded in any unquoted identifier, constant Number, or constant Error. Evaluators shall treat SPACE (U+0020), CHARACTER TABULATION (U+0009), LINE FEED (U+000A), and CARRIAGE RETURN (U+000D) as whitespace characters.
An embedded line break shall be represented by a single LINE FEED character (U+000A), not by a carriage returnlinefeed pair. When embedded in an XML attribute the linefeed character is represented as “
”.
Evaluators should retain whitespace entered by the original formula creator and use it when saving or presenting the formula, and should not add additional whitespace unless directed to do so during the process of editing a formula.
OpenFormula defines commonly used operators and functions.
Function names ignore case. Evaluators should write function names in all uppercase letters when writing OpenFormula formulas.
Unless otherwise noted, if any value being provided is an Error, the result is an Error; if more than one Error is provided, one of them is returned (evaluators should return the leftmost Error result).
For every function or operator, the following are defined in this specification:
Evaluators may extend functions by permitting fewer or additional parameters, which documents may use. Extended functions may result in a lack of interoperability.
●Returns: Return type (e.g., Number, Text, Logical, Reference).
●Constraints: A description of constraints, in addition to the constraints imposed by the parameter types. If there are no additional constraints beyond those imposed by the parameter types, this is "None". If a constraint is not met, the function/operator shall return an Error unless otherwise noted.
●Semantics: This text describes what the function/operator does.
If a parameter is a pseudotype, but the provided value fails to meet the requirements for that type, the behavior is implementationdefined.
Note: Functions and operators are defined by mathematical formulas or by an OpenFormula formula. Formulas define the correct result, and not the algorithm for calculation. Since computing systems have limited precision and range of numbers, some functions cannot or should not be naively implemented as their formulas suggest. This specification defines the mathematically correct answer, and allows implementors to choose the best algorithm that will meet that definition.
●Comment: Explanatory comment.
●See also A list of related operators and functions.
The implicit conversion operators omit many of these items, e.g., the syntax (since there is none).
Any given function or operand takes 0 or more parameters, and each of those parameters has an expected type. The expected type can be one of the base types, identified above. It can also be of some conversion type that controls conversion, e.g., Any means that no conversion is done (it can be of any type); NumberSequence causes a conversion to an ordered sequence of zero or more numbers. If the passedin type does not match the expected type, an attempt is made to automatically convert the value to the expected type. An Error is returned if the type cannot be converted (this can never happen if the expected type is Any). Unless otherwise noted, any conversion operation applied to a value of type Error returns the same value.
To convert to a scalar, if the value is of type:
In some cases a reference to a single cell is needed, but a reference to multiple cells is provided. In this case an "implied intersection" is performed. To perform an implied intersection:
A ForceArray attribute forces calculation of the argument's expression into nonscalar array mode. This means that no implied intersection is performed, instead where a reference to a single cell is expected and multiple cells are provided, iteration over the multiple cells is performed and results are stored in an array that is passed on.
See also NonScalar Evaluation 3.3
If the expected type is Number, then if value is of type:
●Number, return it.
●Logical, return 0 if FALSE, 1 if TRUE.
●Text: The specific conversion is implementationdefined; an evaluator may return 0, an Error value, or the results of its attempt to convert the Text value to a Number (and fall back to 0 or Error if it fails to do so). Evaluators may apply VALUE() or some other function to do this conversion, should they choose to do so. Conversion depends on the actual locale the application runs in, especially if group or decimal separators are involved.
●Reference: If the reference covers more than one cell, do an implied intersection to determine which cell to use. Then obtain the value of the single cell and perform the rules as above. If the calculation setting “precisionasshown” is true, then convert the number to the closest possible representation of the displayed number. If the cell is empty (blank), use 0 (zero) as the value. Evaluators may choose to convert references to Text in a different manner than they handle converting embedded Text to a Number.
If the expected type is Integer for a function or operator, apply the “Conversion to Number” operation. 6.3.5 Then, if the result is a Number but not an integer, apply the specific conversion from Number to integer specified by that particular function/operator. If the function or operator does not specify any particular conversion operation, then the conversion from a noninteger Number into an integer is implementationdefined.
Many different conversions from a noninteger number into an integer are possible. The conversion direction may be towards negative infinity, towards positive infinity, towards zero, away from zero, towards the nearest even number, or towards the nearest odd number. A conversion can select the nearest integer, the nearest even or odd integer, or the “next” integer in the given direction if it is not already an integer. If a conversion selects the nearest integer, a direction is still needed (for when a value is halfway between two integers). In this specification, this conversion is referred to as “rounding” or “truncation”; these terms by themselves do not specify any specific operation.
If a function specifies its rounding operation using a series of capital letters, the function defined in this specification for that function is used to do the conversion to integer. Common such functions are:
●INT, which if given noninteger rounds down to the next integer towards negative infinity, regardless of whether or not it is the closest integer.
●ROUND, which if given noninteger rounds to the nearest integer. If the input number is halfway between integers, it rounds away from zero.
●TRUNC, which if given noninteger rounds towards zero, regardless of whether or not that integer is the closest integer.
If the expected type is NumberSequence, then if value is of type:
●Number, Text, or Logical, handle as Conversion to Number 6.3.5 (creating a sequence of length 1).
●reference, create a sequence of numbers from the values of the referenced cells that only includes the values of type Number or Error. Thus, Empty cells and Text that could be converted into a value is not included in a number sequence. If the Logical type is a distinguished type from the Number type, it should not be included in the sequence of numbers; if the Logical type is not a distinguished type, then such values will (of course) be included in the number sequence.
Identical to Conversion to NumberSequence 6.3.7 , with the addition that instead of a Reference also a ReferenceList is accepted as argument. Each Reference in the list is converted to a NumberSequence in the order of occurrence.
Identical to Conversion to NumberSequence 6.3.7 except that each element in the list represents a serial date value of subtype Date.
An evaluator may accept complex numbers as Text, Number, or a different distinguishable type.
If the value is:
([+]?Number [+])?Number[ij]
[+]?Number[ij]
If the expected type is ComplexSequence, then if value is of type:
If the expected type is Logical, then if value is of type:
If the expected type is LogicalSequence, then if value is of type:
If the expected type is Text, then if value is of type:
If the expected type is the pseudotype DateParam, then if value is of type:
●Number, return it.
●Text, pass to DATEVALUE, and if nonError, return it. If DATEVALUE would return an Error, an evaluator may attempt to convert to a Number in other ways (such as by calling VALUE); this is implementationdefined. If the evaluator cannot convert to Number, it returns an Error.
●Logical, the result is implementationdefined, either a Number or Error
●Reference: perform conversion to scalar, then perform as above. If the cell is empty, return 0.
If the expected type is the pseudotype TimeParam, then if value is of type:
●Number, return it.
●Text, pass to TIMEVALUE, and if nonError, return it. If TIMEVALUE would return an Error, an evaluator may attempt to convert to a Number in other ways (such as by calling VALUE); this is implementationdefined. If the evaluator cannot convert to Number, it returns an Error.
●Logical, the result is implementationdefined, either a Number or Error
●Reference: perform conversion to scalar, then perform as above. If the cell is empty, return 0.
The functions defined under standard operators differ from other functions only by their frequency of use. That frequency of use has lead to the colloquial terminology, standard operators.
Summary: Add two numbers.
Syntax: Number Left + Number Right
Returns: Number
Constraints: None
Semantics: Adds numbers together.
See also Infix Operator "" 6.4.3, Prefix Operator "+" 6.4.15
Summary: Subtract the second number from the first.
Syntax: Number Left  Number Right
Returns: Number
Constraints: None
Semantics: Subtracts one number from another number.
See also Infix Operator "+" 6.4.2, Prefix Operator "" 6.4.16
Summary: Multiply two numbers.
Syntax: Number Left * Number Right
Returns: Number
Constraints: None
Semantics: Multiplies numbers together.
See also Infix Operator "+" 6.4.2, Infix Operator "/" 6.4.5
Summary: Divide the second number into the first.
Syntax: Number Left / Number Right
Returns: Number
Constraints: None
Semantics: Divides numbers. Dividing by zero returns an Error.
See also Infix Operator "" 6.4.3, Infix Operator "*" 6.4.4
Summary: Exponentiation (Power).
Syntax: Number Left ^ Number Right
Returns: Number
Constraints: NOT(AND(Left=0; Right=0)); Evaluators may evaluate expressions where OR(Left != 0; Right != 0) evaluates to a nonError value.
Semantics: Returns POWER(Left, Right).
See also Infix Operator "*" 6.4.4, POWER 6.16.46
Summary: Report if two values are equal
Syntax: Scalar Left = Scalar Right
Returns: Logical
Constraints: None
Semantics: Returns TRUE if two values are equal. If the values differ in type, return FALSE. If the values are both Number, return TRUE if they are considered equal, else return FALSE. If they are both Text, return TRUE if the two values match, else return FALSE. For Text values, if the calculation setting HOSTCASESENSITIVE is false, text is compared but characters differencing only in case are considered equal. If they are both Logicals, return TRUE if they are identical, else return FALSE. Error values cannot be compared to a constant Error value to determine if that is the same Error value.
Evaluators may approximate and test equality of two numeric values with an accuracy of the magnitude of the given values scaled by the number of available bits in the mantissa, ignoring some least significant bits and thus providing compensation for not exactly representable values.
The result of “1=TRUE()” is FALSE for evaluators that implement a distinct Logical type and TRUE if they don't.
See also Infix Operator "<>" 6.4.8
Summary: Report if two values are not equal
Syntax: Any Left <> Any Right
Returns: Logical
Constraints: None
Semantics: Returns NOT(Left = Right) if Left and Right are not Error. For Text values, if the calculation setting HOSTCASESENSITIVE is false, text is compared but characters differencing only in case are considered equal.
If either Left and Right are an Error, the result is an Error; this operator cannot be used to determine if two Errors are the same kind of Error.
Note: In some user interfaces the infix operator “<>” is displayed (or accepted) as “!=” or “≠”.
See also Infix Operator "=" 6.4.7
Summary: Report if two values have the given order
Syntax: Scalar Left op Scalar Right
where op is one of: "<", "<=", ">", or ">="
Returns: Logical
Constraints: None
Semantics: Returns TRUE if the two values are less than, less than or equal, greater than, or greater than or equal (respectively). If both Left and Right are Numbers, compare them as numbers. If both Left and Right are Text, compare them as text; if the calculation setting HOSTCASESENSITIVE is false, text is compared but characters are compared ignoring case. If the values are both Logical, convert both to Number and then compare as Number.
These functions return one of True, False, or an Error if Left and Right have different types, but it is implementationdefined which of these results will be returned when the types differ.
See also Infix Operator "<>" 6.4.8, Infix Operator "=" 6.4.7
Summary: Concatenate two strings.
Syntax: Text Left & Text Right
Returns: Text
Constraints: None
Semantics: Concatenates two text (string) values.
Note: The infix operator “&” is equivalent to CONCATENATE(Left,Right).
See also Infix Operator "+" 6.4.2, CONCATENATE 6.20.6
Summary: Computes an inclusive range given two references
Syntax: Reference Left : Reference Right
Returns: Reference
Constraints: None
Semantics: Takes two references and computes the range, that is, a reference to the smallest 3dimensional cube of cells that include both Left and Right including the cells on sheets positioned between Left and Right. Left and Right need not be a single cell. For an expression such as [.B4:.B5]:[.C5] the resulting range is B4:C5. In case Left and/or Right involve a reference list (result of operator reference union), the range is computed and extended for each element of the list(s).
Note: For example, (a,b,c,d denoting one reference each)
(a~b):(c~d) computes a:b:c:d
determining the outermost fronttopleft and rearbottomright corners.
Left and Right may also be defined names or the result of a function returning a reference, such as INDIRECT.
See also Infix Operator Reference Union 6.4.13, Infix Operator Reference Intersection 6.4.12, INDIRECT 6.14.7
Summary: Compute the intersection of two references
Syntax: Reference Left ! Reference Right
Returns: Reference
Constraints: None
Semantics: Takes two references and computes the intersection  a reference to the intersection of cells in both Left and Right. If there are no cells in common, returns an Error.
If Left or Right are not of type Reference or ReferenceList, an Error shall be returned.
If Left and/or Right are reference lists (result of infix operator reference concatenation), the intersection is computed for each combination of Left and Right, producing a reference list of intersections.
Note 1: For example (a,b,c,d denoting one reference each):
(a~b)!(c~d) will compute (a!c)~(a!d)~(b!c)~(b!d)
If for a resulting intersection there are no cells in common, the element is ignored and omitted from the result list. If for all intersections there are no cells in common and the result list is empty, Error #NULL! is returned.
Note 2: Intersection is notated as "!" in OpenFormula format, but as a space character in some user interfaces.
See also Infix Operator Reference Union 6.4.13
Summary: Concatenate two references
Syntax: Reference Left ~ Reference Right
Returns: ReferenceList
Constraints: None
Semantics: Takes two references and computes the "cell union", which is a concatenation of the reference Left followed by the reference Right. This is not the same as a union in set theory; duplicate references to cells are not removed. The resulting reference will have the number of areas, as reported by AREAS, as AREAS(Left)+AREAS(Right).
Note: Concatenation is notated as "~" in OpenFormula format, but as a comma or “+” in some user interfaces.
If Left or Right are not of type Reference or ReferenceList, an Error shall be returned.
Test Cases:
See also Infix Operator Reference Range 6.4.11, Infix Operator Reference Intersection 6.4.12
Summary: Divide the operand by 100
Syntax: Number Left %
Returns: Number
Constraints: None
Semantics: Computes Left / 100.
See also Prefix Operator "" 6.4.16, Prefix Operator "+" 6.4.15
Summary: No operation; returns its one argument.
Syntax: + Any Right
Returns: Any
Constraints: None
Semantics: Returns the value given to it. Note that this does not convert a value to the Number type. In fact, it does no conversion at all of a Number, Logical, or Text value  it returns the same Number, Logical, or Text value (respectively). The "+" applied to a reference may return the reference, or an Error.
See also Infix Operator "+" 6.4.2
Summary: Negate its one argument.
Syntax:  Number Right
Returns: Number
Constraints: None
Semantics: Computes 0  Right.
See also Infix Operator "" 6.4.3
Matrix functions operate on matrices.
A matrix with M rows and N columns is defined by
Summary: Calculates the determinant of a matrix.
Syntax: MDETERM( ForceArray Array matrix )
Returns: Number
Constraints: Only square matrices are allowed.
Semantics: Returns the determinant of the matrix. The determinant is defined by
where P denotes a permutation of the numbers 1, 2, ..., n and is the sign of the permutation, which is +1 for an even amount of permutations (i.e., permutations that can be written as the composition of an even number of transpositions), 1 otherwise. A transposition on 1, ..., n is a permutation of 1, ..., n with exactly (n2) numbers fixed.
See also MINVERSE 6.5.3
Summary: Returns the inverse of a matrix.
Syntax: MINVERSE( ForceArray Array matrix )
Returns: Array
Constraints: Only square matrices are allowed.
Invertible matrices have a nonzero determinant. If the matrix is not invertible, this function should return an Error value.
See also MDETERM 6.5.2
Summary: Multiplies the matrices A and B.
Syntax: MMULT( ForceArray Array A ; ForceArray Array B )
Returns: Array
Constraints: COLUMNS(A)=ROWS(B)
Summary: Creates a unit matrix of a specified dimension N.
Syntax: MUNIT( Integer N )
Returns: Array
Constraints: The dimension has to be greater than zero.
Semantics: Creates the unit matrix (identity matrix) of dimension N.
Summary: Returns the transpose of a matrix.
Syntax: TRANSPOSE( Array A )
Returns: Array
Constraints: None
Semantics: Returns the transpose AT of a matrix A, i.e. rows and columns of the matrix are exchanged.
Evaluators shall support unsigned integer values and results of at least 48 bits (values from 0 to 2^481 inclusive). Operations that receive or result in a value that cannot be represented within 48 bits are implementationdefined.
Summary: Returns bitwise “and” of its parameters
Syntax: BITAND( Integer X ; Integer Y )
Returns: Number
Constraints: X ≥ 0, Y ≥ 0
Semantics: Returns bitwise “and” of its parameters. In the result, each bit position is 1 if and only if all parameters' bits at that position are also 1; else it is 0.
See also BITOR 6.6.4, BITXOR 6.6.6, AND 6.15.2
Summary: Returns left shift of value x by n bits (“<<”)
Syntax: BITLSHIFT( Integer x ; Integer n )
Returns: Number
Constraints: x ≥ 0
Semantics: Returns left shift of value x by n bit positions:
See also BITAND 6.6.2, BITXOR 6.6.6, BITRSHIFT 6.6.5
Summary: Returns bitwise “or” of its parameters
Syntax: BITOR( Integer X ; Integer Y )
Returns: Number
Constraints: X ≥ 0, Y ≥ 0
Semantics: Returns bitwise “or” of its parameters. In the result, each bit position is 1 if any of its parameters' bits at that position are also 1; else it is 0.
See also BITAND 6.6.2, BITXOR 6.6.6, AND 6.15.2
Summary: Returns right shift of value x by n bits (“>>”)
Syntax: BITRSHIFT( Integer x ; Integer n )
Returns: Number
Constraints: x ≥ 0
Semantics: Returns right shift of value x by n bit positions:
See also BITAND 6.6.2, BITXOR 6.6.6, BITLSHIFT 6.6.3
Summary: Returns bitwise “exclusive or” of its parameters
Syntax: BITXOR( Integer X ; Integer Y )
Returns: Number
Constraints: X ≥ 0, Y ≥ 0
Semantics: Returns bitwise “exclusive or” (xor) of its parameters. In the result, each bit position is 1 if one or the other parameters' bits at that position are 1; else it is 0.
See also BITAND 6.6.2, BITOR 6.6.4, OR 6.15.8
Byteposition text functions are like their equivalent ordinary text functions, but manipulate byte positions rather than a count of the number of characters. Byte positions are integers that may depend on the specific text representation used by the implementation. Byte positions are by definition implementationdependent and reliance upon them reduces interoperability.
The pseudotypes ByteLength and BytePosition are Integers, but their exact meanings and values are not further defined by this specification.
Summary: Returns the starting position of a given text, using byte positions.
Syntax: FINDB( Text Search ; Text T [ ; BytePosition Start ] )
Returns: BytePosition
Semantics: The same as FIND, but using byte positions.
See also FIND 6.20.9 , LEFTB 6.7.3 , RIGHTB 6.7.7
Summary: Returns a selected number of text characters from the left, using a byte position.
Syntax: LEFTB( Text T [ ; ByteLength Length ] )
Returns: Text
Semantics: As LEFT, but using a byte position.
See also LEFT 6.20.12, RIGHT 6.20.19, RIGHTB 6.7.7
Summary: Returns the length of given text in units compatible with byte positions
Syntax: LENB( Text T )
Returns: ByteLength
Constraints: None.
Semantics: As LEN, but compatible with byte position values.
See also LEN 6.20.13, LEFTB 6.7.3, RIGHTB 6.7.7
Summary: Returns extracted text, given an original text, starting position using a byte position, and length.
Syntax: MIDB( Text T ; BytePosition Start ; ByteLength Length )
Returns: Text
Constraints: Length >= 0.
Semantics: As MID, but using byte positions.
See also MID 6.20.15, LEFTB 6.7.3, RIGHTB 6.7.7, REPLACEB 6.7.6
Summary: Returns text where an old text is replaced with a new text, using byte positions.
Syntax: REPLACEB( Text T ; BytePosition Start ; ByteLength Len ; Text New )
Returns: Text
Semantics: As REPLACE, but using byte positions.
See also REPLACE 6.20.17, LEFTB 6.7.3, RIGHTB 6.7.7, MIDB 6.7.5, SUBSTITUTE 6.20.21
Summary: Returns a selected number of text characters from the right, using byte position.
Syntax: RIGHTB( Text T [ ; ByteLength Length ] )
Returns: Text
Semantics: As RIGHT, but using byte positions.
See also RIGHT 6.20.19, LEFTB 6.7.3
Summary: Returns the starting position of a given text, using byte positions.
Syntax: SEARCHB( Text Search ; Text T [ ; BytePosition Start ] )
Returns: BytePosition
Semantics: As SEARCH, but using byte positions.
See also SEARCH 6.20.20, EXACT 6.20.8, FIND 6.20.9, FINDB 6.7.2
Functions for complex numbers.
Summary: Creates a complex number from a given real coefficient and imaginary coefficient.
Syntax: COMPLEX( Number Real ; Number Imaginary [ ; Text Suffix ] )
Returns: Complex
Constraints: None
Semantics: Constructs a complex number by the given coefficients. The third parameter Suffix is optional, and should be either “i” or “j”. Upper case “I” or “J” are not accepted for the suffix parameter.
Summary: Returns the absolute value of a complex number
Syntax: IMABS( Complex X )
Returns: Number
Constraints: None
See also IMARGUMENT 6.8.5
Summary: Returns the imaginary coefficient of a complex number
Syntax: IMAGINARY( Complex X )
Returns: Number
Constraints: None
Semantics: If X=a+bi or X=a+bj, then the imaginary coefficient is b.
See also IMREAL 6.8.19
Summary: Returns the complex argument of a complex number
Syntax: IMARGUMENT( Complex X )
Returns: Number
Constraints: None
Semantics: If X=a+bi=r(cosφ + isinφ), a or b is not 0 and π < φ ≤ π, then the complex argument is φ. φ is expressed by radians. If X=0, then IMARGUMENT(X) is implementationdefined and either 0 or an error.
See also IMABS 6.8.3
Summary: Returns the complex conjugate of a complex number
Syntax: IMCONJUGATE( Complex X )
Returns: Complex
Constraints: None
Semantics: If X=a+bi, then the complex conjugate is abi.
Summary: Returns the cosine of a complex number
Syntax: IMCOS( Complex X )
Returns: Complex
Constraints: None
Semantics: If X=a+bi, then cos(X)=cos(a)cosh(b)sin(a)sinh(b)i.
See also IMSIN 6.8.20
Summary: Returns the hyperbolic cosine of a complex number
Syntax: IMCOSH( Complex N )
Returns: Complex
Constraints: None
Semantics: If N=a+bi, then cosh(N)=cosh(a)cos(b)+sinh(a)sin(b)i.
Summary: Returns the cotangent of a complex number
Syntax: IMCOT(Complex N)
Returns: Complex
Constraints: None
Semantics: Equivalent to the following (except N is computed only once):
IMDIV(IMCOS(N);IMSIN(N))
See also IMTAN 6.8.20
Summary: Returns the cosecant of a complex number
Syntax: IMCSC(Complex N)
Returns: Complex
Constraints: None
Semantics: Equivalent to the following:
IMDIV(1;IMSIN(N))
See also IMSIN 6.8.20
Summary: Returns the hyperbolic cosecant of a complex number
Syntax: IMCSCH( Complex N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic cosecant. This is equivalent to:
IMDIV(1;IMSINH(N))
See also IMSINH, CSCH
Summary: Divides the second number into the first.
Syntax: IMDIV( Complex X ; Complex Y )
Returns: Complex
Constraints: None
Semantics: Given X=a+bi and Y=c+di, return the quotient
Division by zero returns an Error.
See also IMDIV 6.8.12
Summary: Returns the exponent of e and a complex number.
Syntax: IMEXP( Complex X )
Returns: Complex
Constraints: None
See also IMLN 6.8.14
Summary: Returns the natural logarithm of a complex number.
Syntax: IMLN( Complex X )
Returns: Complex
Constraints: X ≠ 0
Semantics: COMPLEX(LN(IMABS(X)); IMARGUMENT(X)) .
See also IMEXP 6.8.13 , IMLOG10 6.8.15
Summary: Returns the common logarithm of a complex number.
Syntax: IMLOG10( Complex X )
Returns: Complex
Constraints: X ≠ 0
Semantics: IMLOG10(X) is IMDIV(IMLN(X);COMPLEX(LN(10);0)) .
See also IMLN 6.8.14 , IMPOWER 6.8.17
Summary: Returns the binary logarithm of a complex number.
Syntax: IMLOG2( Complex X )
Returns: Complex
Constraints: X ≠ 0
Semantics: IMLOG2(X) is IMDIV(IMLN(X);COMPLEX(LN(2);0)) .
See also IMLN 6.8.14 , IMPOWER 6.8.17
Summary: Returns the complex number X raised to the Yth power.
Syntax: IMPOWER( Complex X ; Complex Y ) or IMPOWER( Complex X ; Number Y)
Returns: Complex
Constraints: X ≠ 0
Semantics: IMPOWER(X;Y) is IMEXP(IMPRODUCT(Y; IMLN(X)))
An evaluator implementing this function shall permit any Number Y but may also allow any Complex Y.
See also IMEXP 6.8.13
Summary: Returns the product of complex numbers.
Syntax: IMPRODUCT( { ComplexSequence N }+ )
Returns: Complex
Constraints: None
Semantics: Multiply the complex numbers together. Given two complex numbers X=a+bi and Y=c+di, the product X*Y = (acbd) + (ad+bc)i
See also IMDIV 6.8.12
Summary: Returns the real coefficient of a complex number
Syntax: IMREAL( Complex N )
Returns: Number
Constraints: None
Semantics: If N=a+bi or N=a+bj, then the real coefficient is a.
See also IMAGINARY 6.8.4
Summary: Returns the sine of a complex number
Syntax: IMSIN( Complex N )
Returns: Complex
Constraints: None
Semantics: If N=a+bi, then sin(N)=sin(a)cosh(b)+cos(a)sinh(b)i.
See also IMCOS 6.8.7
Summary: Returns the hyperbolic sine of a complex number
Syntax: IMSINH( Complex N )
Returns: Complex
Constraints: None
Semantics: If N=a+bi, then sinh(N)=sinh(a)cos(b)+cosh(a)sin(b)i.
Summary: Returns the secant of a complex number
Syntax: IMSEC(Complex N)
Returns: Complex
Constraints: None
Semantics: Equivalent to the following:
IMDIV(1;IMCOS(N))
See also IMCOS 6.8.7
Summary: Returns the hyperbolic secant of a complex number
Syntax: IMSECH( Complex N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic secant. This is equivalent to:
IMDIV(1;IMCOSH(N))
See also IMCOSH, SECH
Summary: Returns the square root of a complex number
Syntax: IMSQRT( Complex N )
Returns: Complex
Constraints: None
Semantics: If N= 0+0i, then IMSQRT(N)=0. Otherwise IMSQRT(N) is SQRT(IMABS(N)) * sin(IMARGUMENT(N)/2) + SQRT(IMABS(N)) * cos(IMARGUMENT(N)/2)i.
See also IMPOWER 6.8.17
Summary: Subtracts the second complex number from the first.
Syntax: IMSUB( Complex X ; Complex Y )
Returns: Complex
Constraints: None
Semantics: Subtract complex number Y from X.
See also IMSUM 6.8.26
Summary: Sums (add) a set of complex numbers, including all numbers in ranges
Syntax: IMSUM( { ComplexSequence N }+ )
Returns: Complex Number
Constraints: None
Semantics: Adds complex numbers together. Text that cannot be converted to a complex number is ignored.
It is implementationdefined what happens if this function is given zero parameters; an evaluator may either produce an Error or the Number 0 if it is given zero parameters.
See also IMSUB 6.8.25
Summary: Returns the tangent of a complex number
Syntax: IMTAN(Complex N)
Returns: Complex
Constraints: None
Semantics: Equivalent to the following (except N is computed only once):
IMDIV(IMSIN(N);IMCOS(N))
See also IMSIN, IMCOS, IMCOT 6.8.25
Database functions use the variables, Database 4.11.9, Field 4.11.10, and Criteria 4.11.11.
The results of database functions may change when the values of the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties change. 3.4
Summary: Finds the average of values in a given field from the records (rows) in a database that match a search criteria.
Syntax: DAVERAGE( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform AVERAGE on data records in database D field F that match criteria C.
See also AVERAGE 6.18.3, COUNT 6.13.6, DSUM 6.9.11, DCOUNT 6.9.3, SUM 6.16.61
Summary: Counts the number of records (rows) in a database that match a search criteria and contain numerical values.
Syntax: DCOUNT( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform COUNT on data records in database D field F that match criteria C.
See also COUNT 6.13.6, COUNTA 6.13.7, DCOUNTA 6.9.4, DSUM 6.9.11
Summary: Counts the number of records (rows) in a database that match a search criteria and contain values (as COUNTA).
Syntax: DCOUNTA( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform COUNTA on data records in database D field F that match criteria C.
See also COUNT 6.13.6, COUNTA 6.13.7, DCOUNT 6.9.3, DSUM 6.9.11
Summary: Gets the single value in the field from the single record (row) in a database that matches a search criteria.
Syntax: DGET( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Extracts the value in field F of the one data record in database D that matches criteria C. If no records match, or more than one matches, it returns an Error.
See also DMAX 6.9.6, DMIN 6.9.7, DSUM 6.9.11
Summary: Finds the maximum value in a given field from the records (rows) in a database that match a search criteria.
Syntax: DMAX( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform MAX on only the data records in database D field F that match criteria C.
See also MAX 6.18.45, DMIN 6.9.7, MIN 6.18.48
Summary: Finds the minimum value in a given field from the records (rows) in a database that match a search criteria.
Syntax: DMIN( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform MIN on only the data records in database D field F that match criteria C.
See also MIN 6.18.48, DMAX 6.9.6, MAX 6.18.45
Summary: Finds the product of values in a given field from the records (rows) in a database that match a search criteria.
Syntax: DPRODUCT( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Multiply together only the data records in database D field F that match criteria C.
See also SUM 6.16.61, DSUM 6.9.11
Summary: Finds the sample standard deviation in a given field from the records (rows) in a database that match a search criteria.
Syntax: DSTDEV( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform STDEV on only the data records in database D field F that match criteria C.
See also STDEV 6.18.72, DSTDEVP 6.9.10
Summary: Finds the population standard deviation in a given field from the records (rows) in a database that match a search criteria.
Syntax: DSTDEVP( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform STDEVP on only the data records in database D field F that match criteria C.
See also STDEVP 6.18.74, DSTDEV 6.9.9
Summary: Finds the sum of values in a given field from the records (rows) in a database that match a search criteria.
Syntax: DSUM( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform SUM on only the data records in database D field F that match criteria C.
See also SUM 6.16.61, DMIN 6.9.7, DMAX 6.9.6
Summary: Finds the sample variance in a given field from the records (rows) in a database that match a search criteria.
Syntax: DVAR( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform VAR on only the data records in database D field F that match criteria C.
See also VAR 6.18.82, DVARP 6.9.13
Summary: Finds the population variance in a given field from the records (rows) in a database that match a search criteria.
Syntax: DVARP( Database D ; Field F ; Criteria C )
Returns: Number
Constraints: None
Semantics: Perform VARP on only the data records in database D field F that match criteria C.
See also VARP 6.18.84, DVAR 6.9.12
Summary: Constructs a date from year, month, and day of month.
Syntax: DATE( Integer Year ; Integer Month ; Integer Day )
Returns: Date
Constraints: 1904 <= Year <= 9956; 1 <= Month <= 12; 1 <= Day <= 31; Evaluators may evaluate expressions that do no meet this constraint.
Semantics: This computes the date's serial number given Year, Month, and Day of the Gregorian calendar. Fractional values are truncated. Month > 12 and Day > days of Month will roll over the date, computing the result by adding months and days as necessary. The value of the serial number depends on the current epoch.
See also TIME 6.10.17, DATEVALUE 6.10.4
Summary: Returns the difference in years, months, or days of two date numbers.
Syntax: DATEDIF( DateParam StartDate ; DateParam EndDate ; Text Format )
Returns: Number
Constraints: None
Semantics: Compute difference of StartDate and EndDate, in the units given by Format.
The Format is a code from the following table, entered as text, that specifies the format you want the result of DATEDIF to have.
Table 5  DATEDIF
format  Returns the number of 
y  Years 
m  Months. If there is not a complete month between the dates, 0 will be returned. 
d  Days 
md  Days, ignoring months and years 
ym  Months, ignoring years 
yd  Days, ignoring years 
See also DAYS360 6.10.7, DAYS 6.10.6, Infix Operator “” 6.4.3
Summary: Returns the date serial number from given text.
Syntax: DATEVALUE( Text D )
Returns: Date
Constraints: None
Semantics: This computes the serial number of the text string D, using the current locale. This function shall accept ISO date format (YYYYMMDD), which is localeindependent. It is semantically equal VALUE(Date) if Date has a date format, since text matching a date format is automatically converted to a serial number when used as a Number. If the text of D has a combined date and time format, e.g. YYYYMMDD HH:MM:SS, the integer part of the date serial number is returned. If the text of Date does not have a date or time format, an evaluator may return an Error. See VALUE for more information on date formats. The value of the serial number depends on the current epoch.
See also TIME 6.10.17, DATE 6.10.2, TIMEVALUE 6.10.18, VALUE 6.13.34
Summary: Returns the day from a date.
Syntax: DAY( DateParam Date )
Returns: Number
Constraints: None
Semantics: Returns the day portion of a date.
See also MONTH 6.10.13, YEAR 6.10.23
Summary: Returns the number of days between two dates
Syntax: DAYS( DateParam EndDate ; DateParam StartDate )
Returns: Number
Constraints: None
Semantics: Returns the number of days between two dates. If StartDate and EndDate are Numbers, this is EndDate – StartDate. If they are both Text, this is DATEVALUE(StartDate) – DATEVALUE(EndDate).
See also DATEDIF 6.10.3, DAYS360 6.10.7, MONTH 6.10.13, YEAR 6.10.23, Infix Operator “” 6.4.3
Summary: Returns the number of days between two dates using the 360day year
Syntax: DAYS360( DateParam StartDate ; DateParam EndDate [ ; Integer Method = 0 ] )
Returns: Number
Constraints: 0 <= Method <= 1
Semantics: Returns the number of days between two dates, using the 360day year system (12 30month days). In this system, February always has 30 days and there are no leap years.
If method is 0, it uses the National Association of Securities Dealers (NASD) method, also known as the U.S. method. If the method is 1, the European method is used.
The US/NASD Method (30US/360):
1.Truncate date values, set sign=1.
2.If StartDate's dayofmonth is 31, it is changed to 30.
3.Otherwise, if StartDate's dayofmonth is the last day of February, it is changed to 30.
4.If EndDate's dayofmonth is 31 and StartDate's dayofmonth is 30 (after having applied a change for #2 or #3, if necessary), EndDate's dayofmonth is changed to 30.
Note 1: This calculation is slightly different from Basis 0 (4.11.7 Basis). Dates are never swapped.
The European Method (30E/360):
1.Truncate date values, set sign=1.
2.If StartDate is after EndDate then swap dates and set sign=1.
3.If StartDate's dayofmonth is 31, it is changed to 30.
4.If EndDate's dayofmonth is 31, it is changed to 30.
Note 2: Days in February are never changed.
Note 3: This calculation is identical to Basis 4 (4.11.7 Basis)
For both methods the value then returned is
sign * ((EndDate.year*360 + EndDate.month*30 + EndDate.day)  (StartDate.year*360 + StartDate.month*30 + StartDate.day))
See also DAYS 6.10.6, DATEDIF 6.10.3
Summary: Returns the serial number of a given date when MonthAdd months is added
Syntax: EDATE( DateParam StartDate ; Number MonthAdd )
Returns: Number
Constraints: None
Semantics: First truncate StartDate and MonthAdd, then add MonthAdd number of months. MonthAdd can be positive, negative, or 0; if zero, the number representing StartDate (in the current epoch) is returned.
If after adding the given number of months, the day of month in the new month is larger than the number of days in the given month, the day of month is adjusted to the last day of the new month. Then the serial number of that date is returned.
See also DAYS 6.10.6, DATEDIF 6.10.3, EOMONTH 6.10.9
Summary: Returns the serial number of the end of a month, given date plus MonthAdd months
Syntax: EOMONTH( DateParam StartDate ; Integer MonthAdd )
Returns: Number
Constraints: None
Semantics: First truncate StartDate and MonthAdd, then add MonthAdd number of months. MonthAdd can be positive, negative, or 0. Then return the serial number representing the end of that month. Due to the semantics of this function, the value of DAY(StartDate) is irrelevant.
See also EDATE 6.10.8
Summary: Extracts the hour (0 through 23) from a time.
Syntax: HOUR( TimeParam T )
Returns: Number
Constraints: None
Semantics: Extract from T the hour value, 0 through 23, as per a 24hour clock. This is equal to:
DayFraction=(TINT(T))
Hour=INT(DayFraction*24)
See also MONTH 6.10.13, DAY 6.10.5, MINUTE 6.10.12, SECOND 6.10.16
Summary: Determines the ISO week number of the year for a given date.
Syntax: ISOWEEKNUM( DateParam Date )
Returns: Number
Constraints: None
Semantics: Returns the ordinal number of the [ISO8601] calendar week in the year for the given date. ISO 8601 defines the calendar week as a time interval of seven calendar days starting with a Monday, and the first calendar week of a year as the one that includes the first Thursday of that year.
See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23, WEEKDAY 6.10.20, WEEKNUM 6.10.21
Summary: Extracts the minute (0 through 59) from a time.
Syntax: MINUTE( TimeParam T )
Returns: Number
Constraints: None
Semantics: Extract from T the minute value, 0 through 59, as per a clock. This is equal to:
DayFraction=(TINT(T))
HourFraction=(DayFraction*24INT(DayFraction*24))
Minute=INT(HourFraction*60)
See also MONTH 6.10.13, DAY 6.10.5, HOUR 6.10.10, SECOND 6.10.16
Summary: Extracts the month from a date.
Syntax: MONTH( DateParam Date )
Returns: Number
Constraints: None
Semantics: Takes a date and returns the month portion.
See also YEAR 6.10.23, DAY 6.10.5
Summary: Returns the whole number of work days between two dates.
Syntax: NETWORKDAYS( DateParam Date1 ; DateParam Date2 [ ; [ DateSequence holidays ] [ ; LogicalSequence workdays ] ] )
Returns: Number
Constraints: None
Semantics: Returns the whole number of work days between two dates.
Work days are defined as nonweekend, nonholiday days. By default, weekends are Saturdays and Sundays and there are no holidays.
The optional 3rd parameter Holidays can be used to specify a list of dates to be treated as holidays. Note that this parameter can be omitted as an empty parameter (two consecutive ;; semicolons) to be able to pass the set of Workdays without Holidays.
The optional 4th parameter Workdays can be used to specify a different definition for the standard work week by passing in a list of numbers which define which days of the week are workdays (indicated by 0) or not (indicated by nonzero) in order Sunday, Monday,...,Saturday. So, the default definition of the work week excludes Saturday and Sunday and is: {1;0;0;0;0;0;1}. To define the work week as excluding Friday and Saturday, the third parameter would be: {0;0;0;0;0;1;1}.
Summary: Returns the serial number of the current date and time.
Syntax: NOW()
Returns: DateTime
Constraints: None
Semantics: This returns the current day and time serial number, using the current locale. If you want only the serial number of the current day, use TODAY 6.10.19.
See also DATE 6.10.2, TIME 6.10.17, TODAY 6.10.19
Summary: Extracts the second (the integer 0 through 59) from a time. This function presumes that leap seconds never exist.
Syntax: SECOND( TimeParam T )
Returns: Number
Constraints: None
Semantics: Extract from T the second value, 0 through 59, as per a clock. Note that this returns an integer, without a fractional part. Note also that this rounds to the nearest second, instead of returning the integer part of the seconds. This is equal to:
DayFraction=(TINT(T))
HourFraction=(DayFraction*24INT(DayFraction*24))
MinuteFraction=(HourFraction*60INT(HourFraction*60))
Second=ROUND(MinuteFraction*60)
See also MONTH 6.10.13, DAY 6.10.5, HOUR 6.10.10, MINUTE 6.10.12
Summary: Constructs a time value from hours, minutes, and seconds.
Syntax: TIME( Number hours ; Number minutes ; Number seconds )
Returns: Time
Constraints: None. Evaluators may first perform INT() on the hour, minute, and second before doing the calculation.
Semantics: Returns the fraction of the day consumed by the given time, i.e.:
((hours*60*60)+(minutes*60)+seconds)/(24*60*60)
Time is a subtype of number, where a time value of 1 = 1 day = 24 hours.
Hours, minutes, and seconds may be any number (they shall not be limited to the ranges 0..24, 0..59, or 0..60 respectively).
See also DATE 6.10.2
Summary: Returns a time serial number from given text.
Syntax: TIMEVALUE( Text T )
Returns: Time
Constraints: None
Semantics: This computes the serial number of the text string T, which is a time, using the current locale. This function shall accept ISO time format (HH:MM:SS), which is localeindependent. If the text of T has a combined date and time format, e.g. YYYYMMDD HH:MM:SS, the fractional part of the date serial number is returned. If the text of T does not have a time format, an evaluator may attempt to convert the number another way (e.g., using VALUE), or it may return an Error (this is implementationdependent).
See also TIME 6.10.17, DATE 6.10.2, DATEVALUE 6.10.4, VALUE 6.13.34
Summary: Returns the serial number of today.
Syntax: TODAY()
Returns: Date
Constraints: None
Semantics: This returns the current day's serial number, using current locale. This only returns the date, not the datetime value. For the specific time of day as well, use NOW 6.10.15.
See also TIME 6.10.17, NOW 6.10.15
Summary: Extracts the day of the week from a date; if text, uses current locale to convert to a date.
Syntax: WEEKDAY( DateParam Date [ ; Integer Type = 1 ] )
Returns: Number
Constraints: None
Semantics: Returns the day of the week from a date, as a number from 0 through 7. The exact meaning depends on the value of Type:
1.When Type is 1, Sunday is the first day of the week, with value 1; Saturday has value 7.
2.When Type is 2, Monday is the first day of the week, with value 1; Sunday has value 7.
3.When Type is 3, Monday is the first day of the week, with value 0; Sunday has value 6.
Table 6  WEEKDAY
Day of Week  Type=1 Result  Type=2 Result  Type=3 Result 
Sunday  1  7  6 
Monday  2  1  0 
Tuesday  3  2  1 
Wednesday  4  3  2 
Thursday  5  4  3 
Friday  6  5  4 
Saturday  7  6  5 
See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23
Summary: Determines the week number of the year for a given date.
Syntax: WEEKNUM( DateParam Date [ ; Number Mode = 1 ] )
Returns: Number
Constraints: 1 ≤ Mode ≤ 2, or 11 ≤ Mode ≤ 17, or Mode = 21, or Mode = 150
Semantics: Returns the number of the week in the year for the given date.
For Mode={1, 2, 11, 12, ..., 17} the week containing January 1 is the first week of the year, and is numbered week 1. The week starts on {Sunday, Monday, Monday, Tuesday, ..., Sunday}.
Mode 21 or 150 are both [ISO8601], the week starts on Monday and the week containing the first Thursday of the year is the first week of the year, and is numbered week 1.
See also DAY 6.10.5, MONTH 6.10.13, YEAR 6.10.23, WEEKDAY 6.10.20, ISOWEEKNUM 6.10.11
Summary: Returns the date serial number which is a specified number of work days before or after an input date.
Syntax: WORKDAY( DateParam Date ; Number Offset [ ; [ DateSequence Holidays ] [ ; LogicalSequence Workdays ] ] )
Returns: DateTime
Constraints: None
Semantics: Returns the date serial number for the day that is offset from the input Date parameter by the number of work days specified in the Offset parameter. If Offset is negative, the offset will return a date prior to Date. If Offset is positive, a date later Date is returned. If Offset is zero, then Date is returned.
Work days are defined as nonweekend, nonholiday days. By default, weekends are Saturdays and Sundays and there are no holidays.
The optional 3rd parameter Holidays can be used to specify a list of dates to be treated as holidays. Note that this parameter can be omitted as an empty parameter (two consecutive ;; semicolons) to be able to pass the set of Workdays without Holidays.
The optional 4th parameter Workdays can be used to specify a different definition for the standard work week by passing in a list of numbers which define which days of the week are workdays (indicated by 0) or not (indicated by nonzero) in order Sunday, Monday,...,Saturday. If all seven numbers in Workdays are nonzero and Offset is also nonzero, WORKDAY returns an error.
Note: The default definition of the work week that excludes Saturday and Sunday and is: {1;0;0;0;0;0;1}. To define the workweek as excluding Friday and Saturday, the third parameter would be: {0;0;0;0;0;1;1}.
Summary: Extracts the year from a date given in the current locale of the evaluator.
Syntax: YEAR( DateParam D )
Returns: Number
Constraints: None
Semantics: Parses a dateformatted string in the current locale's format and returns the year portion.
If a year is given as a twodigit number, as in "052115", then the year returned is either 1915 or 2015, depending upon the break point in the calculation context. In an OpenDocument document, this break point is determined by HOSTNULLYEAR.
Evaluators shall support extracting the year from a date beginning in 1900. Threedigit year numbers precede adoption of the Gregorian calendar, and may return either an Error or the year number. Fourdigit year numbers preceding 1582 (inception of the Gregorian Calendar) may return either an Error or the year number. Fourdigit year numbers following 1582 should return the year number.
See also MONTH 6.10.13, DAY 6.10.5, VALUE 6.13.34
Summary: Extracts the number of years (including fractional part) between two dates
Syntax: YEARFRAC( DateParam StartDate ; DateParam EndDate [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: None
Semantics: Computes the fraction of the number of years between a StartDate and EndDate.
Basis indicates the daycount convention to use in the calculation. 4.11.7
See also DATEDIF 6.10.3
OpenFormula defines two functions, DDE and HYPERLINK, for accessing external data.
Summary: Returns data from a DDE request
Syntax: DDE( Text server ; Text topic ; Text item [ ; Integer Mode = 0 ] )
Returns: NumberText
Constraints: None
Semantics: Performs a DDE request and returns its result. The request invokes the service server on the topic named as topic, requesting that it reply with the information on item.
Evaluators may choose to not perform this function on every recalculation, but instead cache an answer and require a separate action to reperform these requests. Evaluators shall perform this request on initial load when their security policies permit it.
Mode is an optional parameter that determines how the results are returned:
Table 7  DDE
Mode  Effect 
0 or missing  Data converted to number using VALUE in the number style's locale of the default table cell style 
1  Data converted to number using VALUE in the EnglishUS (en_US) locale 
2  Data retrieved as text (not converted to number) 
In an OpenDocument spreadsheet document the default table cell style is specified with table:defaultcellstylename. Its number:numberstyle specified by style:datastylename specifies the locale to use in the conversion.
The DDE function is nonportable because it depends on availability of external programs (server parameter) and their interpretation of the topic and item parameters.
Summary: Creation of a hyperlink involving an evaluated expression.
Syntax: HYPERLINK( Text IRI [ ; TextNumber FunctionResult ] )
Returns: Text or Number
Constraints: None
Semantics: The default for the second argument is the value of the first argument. The second argument value is returned.
In addition, hosting environments may interpret expressions containing HYPERLINK function calls as calling for an implementationdependent creation of a hypertext link based on the expression containing the HYPERLINK function calls.
The financial functions are defined for use in financial calculations.
An annuity is a recurring series of payments. A "simple annuity" is one where equal payments are made at equal intervals, and the compounding of interest occurs at those same intervals. The time between payments is called the "payment interval". Where payments are made at the end of the payment interval, it is called an "ordinary annuity". Where payments are made at the beginning of the payment interval, it is called an "annuity due". Periods are numbered starting at 1.
Financial functions defined in this standard use a cash flow sign convention where outgoing cash flows are negative and incoming cash flows are positive.
Summary: Calculates the accrued interest for securities with periodic interest payments.
Syntax: ACCRINT( DateParam issue ; DateParam first ; DateParam settlement ; Number coupon ; Number par ; Integer frequency [ ; Basis basis = 0 [ ; Logical calc_method = TRUE() ] ] )
Returns: Currency
Constraints: issue < first < settlement ; coupon > 0; par > 0
frequency is one of the following values:
Table 8  ACCRINT
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
12  Monthly 
Semantics: Calculates the accrued interest for securities with periodic interest payments. ACCRINT supports short, standard, and long coupon periods.
If calc_method is TRUE (the default) then ACCRINT returns the sum of the accrued interest in each coupon period from issue date until settlement date. If calc_method is FALSE then ACCRINT returns the sum of the accrued interest in each coupon period from first date until settlement date. For each coupon period, the interest is par*coupon*YEARFRAC(startofperiod;endofperiod; basis)
issue The security's issue or dated date.
first The security's first interest date.
settlement The security's settlement date.
coupon The security's annual coupon rate.
par The security's par value, that is, the principal to be paid at maturity.
frequency The number of coupon payments per year.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
calc_method A logical value that specifies how to treat the case where settlement>first.
See also ACCRINTM 6.12.3
Summary: Calculates the accrued interest for securities that pay at maturity.
Syntax: ACCRINT( DateParam issue ; DateParam settlement ; Number coupon ; Number par [ ; Basis basis = 0 ] )
Returns: Currency
Constraints: coupon > 0; par > 0
Semantics: Calculates the accrued interest for securities that pay at maturity.
issue The security's issue or dated date.
settlement The security's maturity date.
coupon The security's annual coupon rate.
par The security's par value, that is, the principal to be paid at maturity.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also ACCRINT 6.12.2
Summary: Calculates the amortization value for the French accounting system using linear depreciation (l'amortissement linéaire comptable) .
Syntax: AMORLINC( Number cost ; DateParam purchaseDate ; DateParam firstPeriodEndDate ; Number salvage ; Integer period ; Number rate [ ; Basis basis = 0 ] )
Returns: Currency
Constraints: cost > 0; purchaseDate <= firstPeriodEndDate; salvage >= 0; period >= 0; rate > 0
Semantics: Calculates the amortization value for the French accounting system using linear depreciation.
cost The value of the asset at the date of aquisition.
purchaseDate The date of aquisition.
firstPeriodEndDate The end date of the first depreciation period.
salvage The value of the asset at the end of the depreciation life time.
period Which period the depreciation should be calculated for.
rate The rate of depreciation.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
When period = 0:
For full periods, where period > 0, the depreciation is cost * rate
For the last period, possibly a partial period, the depreciation = costsalvageaccumulateddepreciation, where accumulateddepreciation is the sum of the depreciation in period 0 plus any full period depreciations.
When period > depreciated life of the asset, i.e., when period > (costsalvage)/(cost*rate) then the depreciation is 0.
Note: The behavior of this function is implementationdefined in cases where purchaseDate = firstPeriodEndDate.
See also DB 6.12.13, DDB 6.12.14, YEARFRAC 6.10.24
Summary: Calculates the number of days between the beginning of the coupon period that contains the settlement date and the settlement date.
Syntax: COUPDAYBS( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Number
Constraints: settlement < maturity
frequency is one of the following values:
Table 9  COUPDAYBS
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculate the number of days from the beginning of the coupon period to the settlement date.
settlement The settlement date.
maturity The maturity date.
frequency The number of coupon payments per year.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also COUPDAYS 6.12.6 , COUPDAYSNC 6.12.7 , COUPNCD 6.12.7 , COUPNUM 6.12.9 , COUPPCD 6.12.10
Summary: Calculates the number of days in a coupon period that contains the settlement date.
Syntax: COUPDAYS( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Number
Constraints: settlement < maturity
frequency is one of the following values:
Table 10  COUPDAYS
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculates the number of days in the coupon period containing the settlement date.
settlement The settlement date.
maturity The maturity date.
frequency The number of coupon payments per year.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also COUPDAYBS 6.12.5 , COUPDAYSNC 6.12.7 , COUPNCD 6.12.7 , COUPNUM 6.12.9 , COUPPCD 6.12.10
Summary: Calculates the number of days between a settlement date and the next coupon date.
Syntax: COUPDAYNC( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Number
Constraints: settlement < maturity
frequency is one of the following values:
Table 11  COUPDAYSNC
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculates the number of days between the settlement date and the next coupon date.
settlement The settlement date.
maturity The maturity date.
frequency The number of coupon payments per year.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also COUPDAYBS 6.12.5 , COUPDAYS 6.12.6 , COUPNCD 6.12.7 , COUPNUM 6.12.9 , COUPPCD 6.12.10
Summary: Calculates the next coupon date following a settlement.
Syntax: COUPNCD( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Date
Constraints: settlement < maturity
frequency is the number of coupon payments per year. frequency is one of the following values:
Table 12  COUPNCD
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculates the next coupon date after the settlement date based on the maturity (expiration) date of the asset, the frequency of coupon payments and the daycount basis.
Basis indicates the daycount convention to use in the calculation. 4.11.7
Summary: Calculates the number of outstanding coupons between settlement and maturity dates.
Syntax: COUPNUM( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Number
Constraints: frequency is the number of coupon payments per year. frequency is one of the following values:
Table 13  COUPNUM
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculates the number of coupons in the interval between the settlement and the maturity (expiration) date of the asset, the frequency of coupon payments and the daycount basis.
Basis indicates the daycount convention to use in the calculation. 4.11.7
See also COUPDAYBS 6.12.5, COUPDAYS 6.12.6, COUPDAYSNC 6.12.7, COUPNCD 6.12.7, COUPPCD 6.12.10
Summary: Calculates the next coupon date prior a settlement.
Syntax: COUPPCD( DateParam settlement ; DateParam maturity ; Integer frequency [ ; Basis basis = 0 ] )
Returns: Date
Constraints: settlement < maturity
frequency is the number of coupon payments per year. frequency is one of the following values:
Table 14  COUPPCD
frequency  Frequency of coupon payments 
1  Annual 
2  Semiannual 
4  Quarterly 
Semantics: Calculates the next coupon date prior to the settlement date based on the maturity (expiration) date of the asset, the frequency of coupon payments and the daycount basis.
Basis indicates the daycount convention to use in the calculation. 4.11.7
See also COUPDAYBS 6.12.5, COUPDAYS 6.12.6, COUPDAYSNC 6.12.7, COUPNCD 6.12.7, COUPNUM 6.12.9
Summary: Calculates a cumulative interest payment.
Syntax: CUMIPMT( Number rate ; Number periods ; Number value ; Integer start ; Integer end ; Integer type )
Returns: Currency
Constraints: rate > 0; value > 0; 1 <= start <= end <= periods
type is one of the following values:
Table 15  CUMIPMT
type  Maturity date 
0  due at the end 
1  due at the beginning 
Semantics: Calculates the cumulative interest payment.
rate The interest rate per period.
periods The number of periods.
value The current value of the loan.
start The starting period.
end The end period.
type The maturity date, the beginning or the end of a period.
See also IPMT 6.12.23, CUMPRINC 6.12.12
Summary: Calculates a cumulative principal payment.
Syntax: CUMPRINC( Number rate ; Number periods ; Number value ; Integer start ; Integer end ; Integer type )
Returns: Currency
Constraints: type is one of the following values:
Table 16  CUMPRINC
type  Maturity date 
0  due at the end 
1  due at the beginning 
Semantics: Calculates the cumulative principal payment.
rate The interest rate per period.
periods The number of periods.
value The current value of the loan.
start The starting period.
end The end period.
type The maturity date, the beginning or the end of a period.
See also PPMT 6.12.37 , CUMIPMT 6.12.11
Summary: Compute the depreciation allowance of an asset.
Syntax: DB( Number cost ; Number salvage ; Integer lifeTime ; Number period [ ; Number month = 12 ] )
Returns: Currency
Constraints: cost > 0, salvage >= 0, lifetime >0; period > 0; 0 < month < 13
Semantics: Calculate the depreciation allowance of an asset with an initial value of cost, an expected useful lifeTime, and a final salvage value at a specified period of time, using the fixeddeclining balance method. The parameters are:
The rate is calculated as follows:
and is rounded to 3 decimals.
For the first period the residual value is
For all periods, where period <= lifeTime, the residual value is calculated by
If month was specified, the residual value for the period after lifeTime becomes
The depreciation allowance for the first period is
For all other periods the allowance is calculated by
For all periods, where period > lifeTime + 1 – INT(month/12), the depreciation allowance is zero.
See also DDB 6.12.14, SLN 6.12.45
Summary: Compute the amount of depreciation at a given period of time.
Syntax: DDB( Number cost ; Number salvage ; Number lifeTime ; Number period [ ; Number declinationFactor = 2 ] )
Returns: Currency
Constraints: cost >= 0, salvage >= 0, salvage <= cost, 1 <= period <= lifeTime, declinationFactor > 0
Semantics: Compute the amount of depreciation of an asset at a given period of time. The parameters are:
To calculate depreciation, DDB uses a fixed rate. When declinationFactor = 2 this is the doubledecliningbalance method (because it is double the straightline rate that would depreciate the asset to zero). The rate is given by:
The depreciation each period is calculated as
depreciation_of_period = MIN( book_value_at_start_of_ period * rate; book_value_at_start_of_ period  salvage )
Thus the asset depreciates at rate until the book value is salvage value.
To allow also noninteger period values this algorithm may be used:
If period is an Integer number, the relation between DDB and VDB is:
DDB( cost ; salvage ; lifeTime ; period ; declinationFactor )
equals
VDB( cost ; salvage ; lifeTime ; period  1 ; period ; declinationFactor ; TRUE() )
See also SLN 6.12.45, VDB 6.12.50
Summary: Returns the discount rate of a security.
Syntax: DISC( DateParam settlement ; DateParam maturity ; Number price ; Number redemption [ ; Basis basis = 0 ] )
Returns: Percentage
Constraints: settlement < maturity
Semantics: Calculates the discount rate of a security.
settlement The settlement date of the security.
maturity The maturity date.
price The price of the security.
redemption The redemption value of the security.
basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also YEARFRAC 6.10.24
Summary: Converts a fractional dollar representation into a decimal representation.
Syntax: DOLLARDE( Number fractional ; Integer denominator )
Returns: Number
Constraints: denominator > 0
Semantics: Converts a fractional dollar representation into a decimal representation.
fractional Decimal fraction.
denominator Denominator of the fraction.
See also DOLLARFR 6.12.17 , TRUNC 6.17.8
Summary: Converts a decimal dollar representation into a fractional representation.
Syntax: DOLLARFR( Number decimal ; Integer denominator )
Returns: Number
Constraints: denominator > 0
Semantics: Converts a decimal dollar representation into a fractional representation.
decimal Decimal number.
denominator Denominator of the fraction.
See also DOLLARDE 6.12.16, TRUNC 6.17.8
Summary: Returns the Macaulay duration of a fixed interest security in years
Syntax: DURATION( Date Settlement ; Date Maturity ; Number Coupon ; Number Yield ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Yield >=0, Coupon >= 0, Settlement <= Maturity; Frequency = 1, 2, 4
Semantics: Computes the Macaulay duration, given:
Settlement the date of purchase of the securityMaturity the date when the security matures
Coupon the annual nominal rate of interest
Yield the annual yield of the security
Frequency number of interest payments per year
Basis Basis indicates the daycount convention to use in the calculation. 4.11.7
See also MDURATION 6.12.26
Summary: Returns the net annual interest rate for a nominal interest rate.
Syntax: EFFECT( Number rate ; Integer payments )
Returns: Number
Constraints: rate >= 0; payments > 0
Semantics: Nominal interest refers to the amount of interest due at the end of a calculation period. Effective interest increases with the number of payments made. In other words, interest is often paid in installments (for example, monthly or quarterly) before the end of the calculation period.
rate The interest rate per period.
payments The number of payments per period.
See also NOMINAL 6.12.28
Summary: Compute the future value (FV) of an investment.
Syntax: FV( Number Rate ; Number Nper ; Number Payment [ ; [ Number Pv = 0 ] [ ; Number PayType = 0 ] ] )
Returns: Currency
Constraints: None.
Semantics: Computes the future value of an investment. The parameters are:
See PV 6.12.41 for the equation this solves.
See also PV 6.12.41, NPER 6.12.29, PMT 6.12.36, RATE 6.12.42
Summary: Returns the accumulated value given starting capital and a series of interest rates.
Syntax: FVSCHEDULE( Number Principal ; NumberSequence Schedule )
Returns: Currency
Constraints: None.
Semantics: Returns the accumulated value given starting capital and a series of interest rates, as follows:
See also PV 6.12.41, NPER 6.12.29, PMT 6.12.36, RATE 6.12.42
Summary: Computes the interest rate of a fully vested security.
Syntax: INTRATE( Date Settlement ; Date Maturity ; Number Investment ; Number Redemption [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Settlement < Maturity
Semantics: Calculates the annual interest rate that results when an item is purchased at the investment price and sold at the redemption price. No interest is paid on the investment. The parameters are:
Settlement: the date of purchase of the security.Maturity: the date on which the security is sold.
Investment: the purchase price.
Redemption: the selling price.
Basis indicates the daycount convention to use in the calculation. 4.11.7
The return value for this function is:
See also RECEIVED 6.12.43, YEARFRAC 6.10.24
Summary: Returns the amount of an annuity payment going towards interest.
Syntax: IPMT( Number Rate ; Number Period ; Number Nper ; Number PV [ ; Number FV = 0 [ ; Number Type = 0 ] ] )
Returns: Currency
Constraints: None.
Semantics: Computes the interest portion of an amortized payment for a constant interest rate and regular payments. The interest payment is the interest rate multiplied by the balance at the beginning of the period. The parameters are:
Rate: The periodic interest rate.
Period: The period for which the interest payment is computed.
Nper: The total number of periods for which the payments are made
PV: The present value (e.g. The initial loan amount).
FV: The future value (optional) at the end of the periods. Zero if omitted.
Type: the due date for the payments (optional). Zero if omitted. If type is 1, then payments are made at the beginning of each period. If type is 0, then payments are made at the end of each period.
See also PPMT 6.12.37, PMT 6.12.36
Summary: Compute the internal rate of return for a series of cash flows.
Syntax: IRR( NumberSequence Values [ ; Number Guess = 0.1 ] )
Returns: Percentage
Constraints: None.
Semantics: Compute the internal rate of return for a series of cash flows.
If provided, Guess is an estimate of the interest rate to start the iterative computation. If omitted, the value 0.1 (10%) is assumed.
The result of IRR is the rate at which the NPV() function will return zero with the given values.
There is no closed form for IRR. Evaluators may return an approximate solution using an iterative method, in which case the Guess parameter may be used to initialize the iteration. If the evaluator is unable to converge on a solution given a particular Guess, it may return an Error.
See also NPV 6.12.30, RATE 6.12.42
Summary: Compute the interest payment of an amortized loan for a given period.
Syntax: ISPMT( Number Rate ; Number Period ; Number Nper ; Number Pv )
Returns: Currency
Constraints: None.
Semantics: Computes the interest payment of an amortized loan for a given period. The parameters are:
See also PV 6.12.41, FV 6.12.20, NPER 6.12.29, PMT 6.12.36, RATE 6.12.42
Summary: Returns the modified Macaulay duration of a fixed interest security in years
Syntax: MDURATION( Date Settlement ; Date Maturity ; Number Coupon ; Number Yield ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Yield >= 0, Coupon >= 0, Settlement <= Maturity; Frequency = 1, 2, 4
Semantics: Computes the modified Macaulay duration, given:
The modified duration is computed as follows:
See also DURATION 6.12.18
Summary: Returns the modified internal rate of return (IRR) of a series of periodic investments
Syntax: MIRR( Array Values ; Number Investment ; Number ReinvestRate )
Returns: Percentage
Constraints: Values shall contain at least one positive value and at least one negative value.
Semantics: Values is a series of periodic income (positive values) and payments (negative values) at regular intervals (Text and Empty cells are ignored). Investment is the rate of interest of the payments (negative values); ReinvestRate is the rate of interest of the reinvestment (positive values).
Computes the modified internal rate of return, which is:
where N is the number of incomes and payments in Values (total).
See also IRR 6.12.24
Summary: Compute the annual nominal interest rate.
Syntax: NOMINAL( Number EffectiveRate ; Integer CompoundingPeriods )
Returns: Number
Constraints: EffectiveRate >0 , CompoundingPeriods > 0
Semantics: Returns the annual nominal interest rate based on the effective rate and the number of compounding periods in one year. The parameters are:
Suppose that P is the present value, m is the compounding periods per year, the future value after one year is
The mapping between nominal rate and effective rate is
See also EFFECT 6.12.19
Summary: Compute the number of payment periods for an investment.
Syntax: NPER( Number Rate ; Number Payment ; Number Pv [ ; [ Number Fv ] [ ; Number PayType ] ] )
Returns: Number
Constraints: None.
Semantics: Computes the number of payment periods for an investment. The parameters are:
If Rate is 0, then NPER solves this equation:
If Rate is nonzero, then NPER solves this equation:
Evaluators claiming to support the “Medium” or “Large” set shall support negative rates; evaluators only claiming to support the “Small” set need not.
See also FV 6.12.20, RATE 6.12.42, PMT 6.12.36, PV 6.12.41
Summary: Compute the net present value (NPV) for a series of periodic cash flows.
Syntax: NPV( Number Rate ; { NumberSequenceList Value }+ )
Returns: Currency
Constraints: None.
Semantics: Computes the net present value for a series of periodic cash flows with the discount rate Rate. Values should be positive if they are received as income, and negative if the amounts are paid as outgo. Because the result is affected by the order of values, evaluators shall evaluate arguments in the order given and range reference and array arguments rowwise starting from top left.
If n is the number of values in the Values, the formula for NPV is:
See also FV 6.12.20, IRR 6.12.24, NPER 6.12.29, PMT 6.12.36, PV 6.12.41, XNPV 6.12.52
Summary: Compute the value of a security per 100 currency units of face value. The security has an irregular first interest date.
Syntax: ODDFPRICE( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; DateParam First ; Number Rate ; Number Yield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, Yield, and Redemption should be greater than 0.
Semantics: The parameters are
See also ODDLPRICE 6.12.33 , ODDFYIELD 6.12.32
Summary: Compute the yield of a security per 100 currency units of face value. The security has an irregular first interest date.
Syntax: ODDFYIELD( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; DateParam First ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, Price, and Redemption should be greater than 0. Maturity > First > Settlement > Issue.
Semantics: The parameters are
See also ODDLYIELD 6.12.34 , ODDFPRICE 6.12.31
Summary: Compute the value of a security per 100 currency units of face value. The security has an irregular last interest date.
Syntax: ODDLPRICE( DateParam Settlement ; DateParam Maturity ; DateParam Last ; Number Rate ; Number AnnualYield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, AnnualYield, and Redemption should be greater than 0. The Maturity date should be greater than the Settlement date, and the Settlement should be greater than the last interest date.
Semantics: The parameters are
See also ODDFPRICE 6.12.31
Summary: Compute the yield of a security which has an irregular last interest date.
Syntax: ODDLYIELD( DateParam Settlement ; DateParam Maturity ; DateParam Last ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, Price, and Redemption should be greater than 0.
Semantics: The parameters are
See also ODDLPRICE 6.12.33 , ODDFYIELD 6.12.32
Summary: Returns the number of periods required by an investment to realize a specified value.
Syntax: PDURATION( Number rate ; Number currentValue ; Number specifiedValue )
Returns: Number
Constraints: rate > 0; currentValue > 0; specifiedValue > 0
Semantics: Calculates the number of periods for attaining a certain value specifiedValue, starting from currentValue and using the interest rate rate.
See also DURATION 6.12.18
Summary: Compute the payment made each period for an investment.
Syntax: PMT( Number Rate ; Integer Nper ; Number Pv [ ; [ Number Fv = 0 ] [ ; Number PayType = 0 ] ] )
Returns: Currency
Constraints: Nper > 0
Semantics: Computes the payment made each period for an investment. The parameters are:
If Rate is 0, the following equation is solved:
If Rate is nonzero, then PMT solves this equation:
See also FV 6.12.20, NPER 6.12.29, PV 6.12.41, RATE 6.12.42
Summary: Calculate the payment for a given period on the principal for an investment at a given interest rate and constant payments.
Syntax: PPMT( Number Rate ; Integer Period ; Integer nPer ; Number Present [ ; Number Future = 0 [ ; Number Type = 0 ] ] )
Returns: Number
Constraints: Rate and Present should be greater than 0. 0<Period <nPer.
Semantics: The parameters are
See also PMT 6.12.36
Summary: Calculates a quoted price for an interest paying security, per 100 currency units of face value.
Syntax: PRICE( DateParam Settlement ; DateParam Maturity ; Number Rate ; Number AnnualYield ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, AnnualYield, and Redemption should be greater than 0; Frequency = 1, 2 or 4.
Semantics: If A is the number of days from the Settlement date to next coupon date, B is the number of days of the coupon period that the Settlement is in, C is the number of coupons between Settlement date and Redemption date, D is the number of days from beginning of coupon period to Settlement date, then PRICE is calculated as
The parameters are
See also PRICEDISC 6.12.39, PRICEMAT 6.12.40
Summary: Calculate the price of a security with a discount per 100 currency units of face value.
Syntax: PRICEDISC( DateParam Settlement ; DateParam Maturity ; Number Discount ; Number Redemption [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Discount and Redemption should be greater than 0.
Semantics: The parameters are
See also PRICE 6.12.38, PRICEMAT 6.12.40, YIELDDISC 6.12.54
Summary: Calculate the price per 100 currency units of face value of the security that pays interest on the maturity date.
Syntax: PRICEMAT( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; Number Rate ; Number AnnualYield [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Settlement < Maturity, Rate >= 0, AnnualYield >= 0
Semantics: The parameters are
If both, Rate and AnnualYield, are 0, the return value is 100.
See also PRICEDISC 6.12.39, PRICEMAT 6.12.40
Summary: Compute the present value (PV) of an investment.
Syntax: PV( Number Rate ; Number Nper ; Number Payment [ ; [ Number Fv = 0 ] [ ; Number PayType = 0 ] ] )
Returns: Currency
Constraints: None.
Semantics: Computes the present value of an investment. The parameters are:
If Rate is 0, then:
If Rate is nonzero, then PV solves this equation:
See also FV 6.12.20, NPER 6.12.29, PMT 6.12.36, RATE 6.12.42
Summary: Compute the interest rate per period of an investment.
Syntax: RATE( Number Nper ; Number Payment ; Number Pv [ ; [ Number Fv = 0 ] [ ; [ Number PayType = 0 ] [ ; Number Guess = 0.1 ] ] ] )
Returns: Percentage
Constraints: If Nper is 0 or less than 0, the result is an Error.
Semantics: Computes the interest rate of an investment. The parameters are:
RATE solves this equation:
See also FV 6.12.20, NPER 6.12.29, PMT 6.12.36, PV 6.12.41
Summary: Calculates the amount received at maturity for a zero coupon bond.
Syntax: RECEIVED( DateParam Settlement ; DateParam Maturity ; Number Investment ; Number Discount [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Investment and Discount should be greater than 0.
Semantics:
The parameters are
The return value is:
See also YEARFRAC 6.10.24
Summary: Returns an equivalent interest rate when an investment increases in value.
Syntax: RRI( Number N ; Number Pv ; Number Fv )
Returns: Percentage
Constraints: N > 0
Semantics: Returns the interest rate given N (the number of periods), Pv (present value), and Fv (future value), calculated as follows:
See also FV 6.12.20, NPER 6.12.29, PMT 6.12.36, PV 6.12.41, RATE 6.12.42
Summary: Compute the amount of depreciation at a given period of time using the straightline depreciation method.
Syntax: DDB( Number Cost ; Number Salvage ; Number LifeTime )
Returns: Currency
Constraints: None.
Semantics: Compute the amount of depreciation of an asset at a given period of time using straightline depreciation. The parameters are:
For alternative methods to compute depreciation, see DDB 6.12.14.
See also DDB 6.12.14
Summary: Compute the amount of depreciation at a given period of time using the SumoftheYears'Digits method.
Syntax: SYD( Number Cost ; Number Salvage ; Number LifeTime ; Number Period )
Returns: Currency
Constraints: None.
Semantics: Compute the amount of depreciation of an asset at a given period of time using the SumoftheYears'Digits method. The parameters are:
For other methods of computing depreciation, see DDB 6.12.14.
See also SLN 6.12.45, DDB 6.12.14
Summary: Compute the bondequivalent yield for a treasury bill.
Syntax: TBILLEQ( DateParam Settlement ; DateParam Maturity ; Number Discount )
Returns: Number
Constraints: The maturity date should be less than one year beyond settlement date. Discount is any positive value.
Semantics: The parameters are defined as,
TBILLEQ is calculated as
where DSM is the number of days between settlement and maturity computed according to the 360 days per year basis (basis 2, 4.11.7)
See also TBILLPRICE 6.12.48, TBILLYIELD 6.12.49
Summary: Compute the price per 100 face value for a treasury bill.
Syntax: TBILLPRICE( DateParam Settlement ; DateParam Maturity ; Number Discount )
Returns: Number
Constraints: The maturity date should be less than one year beyond settlement. Discount is any positive value.
Semantics: The parameters are:
See also TBILLEQ 6.12.47, TBILLYIELD 6.12.49
Summary: Compute the yield for a treasury bill.
Syntax: TBILLYIELD( DateParam Settlement ; DateParam Maturity ; Number Price )
Returns: Number
Constraints: The maturity date should be less than one year beyond settlement. Price is any positive value.
Semantics: The parameters are:
See also TBILLEQ 6.12.47, TBILLPRICE 6.12.48
Summary: Calculates the depreciation allowance of an asset with an initial value, an expected useful life, and a final value of salvage for a period specified, using the variablerate declining balance method..
Syntax: VDB( Number cost ; Number salvage ; Number lifeTime ; Number startPeriod ; Number endPeriod [ ; Number depreciationFactor = 2 [ ; Logical noSwitch = FALSE() ] ] )
Returns: Number
Constraints: salvage < cost, lifeTime > 0, 0 ≤ startPeriod ≤ lifeTime, startPeriod ≤ endPeriod ≤ lifeTime, depreciationFactor ≥ 0
Semantics: cost is the amount paid for the asset. cost can be any value greater than salvage.
salvage is the value of the asset at the end of its life. salvage can be any value.
lifeTime is the number of periods the asset takes to depreciate to its salvage value. lifeTime can be any value greater than 0.
startPeriod is the point in the asset's life when you want to begin calculating depreciation. startPeriod can be any value greater than or equal to 0, but cannot be greater than lifeTime.
endPeriod is the point in the asset's life when you want to stop calculating depreciation. endPeriod can be any value greater than startPeriod.
startPeriod and endPeriod correspond to the asset's life, relative to the fiscal period. For example, if you want to find the first year's depreciation of an asset purchased at the beginning of the second quarter of a fiscal year, startperiod would be 0 and endperiod would be 0.75 (1 minus 0.25 of a year).
VDB allows for the use of an initialPeriod option to calculate depreciation for the period the asset is placed in service. VDB uses the fractional part of startPeriod and endPeriod to determine the initialPeriod option. If both startPeriod and endPeriod have fractional parts, then VDB uses the fractional part of startPeriod.
depreciationFactor is an optional argument that specifies the percentage of straightline depreciation you want to use as the depreciation rate. If you omit this argument, VDB uses 2, which is the doubledeclining balance rate. depreciationfactor can be any value greater than or equal to 0; commonly used rates are 1.25, 1.50, 1.75, and 2.
noSwitch is an optional argument that you include if you do not want VDB to switch to straightline depreciation for the remaining useful life. Normally, decliningbalance switches to such a straightline calculation when it is greater than the decliningbalance calculation.
If noSwitch is FALSE() or omitted, VDB automatically switches to straightline depreciation when that is greater than decliningbalance depreciation. If noSwitch is TRUE(), VDB never switches to straightline depreciation.
See also DDB 6.12.14, SLN 6.12.45
Summary: Compute the internal rate of return for a nonperiodic series of cash flows.
Syntax: XIRR( NumberSequence Values ; DateSequence Dates [ ; Number Guess = 0.1 ] )
Returns: Number
Constraints: The size of Values and Dates are equal. Values contains at least one positive and one negative cash flow.
Semantics: Compute the internal rate of return for a series of cash flows which is not necessarily periodic. The parameters are
See also IRR 6.12.24
Summary: Compute the net present value of a series of cash flows.
Syntax: XNPV( Number Rate ; ReferenceArray Values ; Reference Array Dates )
Returns: Number
Constraints:
Number of elements in Values equals number of elements in Dates.
All elements of Values are of type Number.
All elements of Dates are of type Number.
All elements of Dates >= Dates[1]
Semantics: Compute the net present value for a series of cash flows which is not necessarily periodic. The parameters are
With N being the number of elements in Values and Dates each, the formula is:
See also NPV 6.12.30
Summary: Calculate the yield of a bond.
Syntax: YIELD( DateParam Settlement ; DateParam Maturity ; Number Rate ; Number Price ; Number Redemption ; Number Frequency [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate, Price, and Redemption should be greater than 0.
Semantics: The parameters are
See also PRICE 6.12.38, YIELDDISC 6.12.54, YIELDMAT 6.12.55
Summary: Calculate the yield of a discounted security per 100 currency units of face value.
Syntax: YIELDDISC( DateParam Settlement ; DateParam Maturity ; Number Price ; Number Redemption [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Price and Redemption should be greater than 0.
Semantics: The parameters are
The return value is
See also PRICEDISC 6.12.39, YEARFRAC 6.10.24
Summary: Calculate the yield of the security that pays interest on the maturity date.
Syntax: YIELDMAT( DateParam Settlement ; DateParam Maturity ; DateParam Issue ; Number Rate ; Number Price [ ; Basis Basis = 0 ] )
Returns: Number
Constraints: Rate and Price should be greater than 0.
Semantics: The parameters are
See also PRICE 6.12.38, YIELD 6.12.53, YIELDDISC 6.12.54
Information functions provide information about a data value, the spreadsheet, or underlying environment, including special functions for converting between data types.
Summary: Returns the number of areas in a given reference
Syntax: AREAS( ReferenceList R )
Returns: Number
Constraints: None
Semantics: Returns the number of areas in the reference list.
See also Infix Operator Reference Concatenation 6.4.13, INDEX 6.14.6
Summary: Returns information about position, formatting or contents in a reference.
Syntax: CELL( Text Info_Type [ ; Reference R ] )
Returns: Information about position, formatting properties or content
Constraints: None
Semantics: The parameters are
Table 17  CELL
Info_Type  Comment 
COL  Returns the column number of the cell. 
ROW  Returns the row number of the cell. 
SHEET  Returns the sheet number of the cell. 
ADDRESS  Returns the absolute address of the cell. The sheet name is included if given in the reference. For an external reference a Source as specified in the syntax rules for References 5.8 is included. 
FILENAME  Returns the file name of the file that contains the cell as an IRI. If the file is newly created and has not yet been saved, the file name is empty text “”. 
CONTENTS  Returns the contents of the cell, without formatting properties. 
COLOR  Returns 1 if color formatting is set for negative value in this cell; otherwise returns 0 
FORMAT  Returns a text string which shows the number format of the cell. ,(comma) = number with thousands separator F = number without thousands separator C = currency format S = exponential representation P = percentage To indicate the number of decimal places after the decimal separator, a number is given right after the above characters. D1 = MMMDYY, MMDYY and similar formats D2 = DDMM D3 = MMYY D4 = DDMMYYYY HH:MM:SS D5 = MMDD D6 = HH:MM:SS AM/PM D7 = HH:MM AM/PM D8 = HH:MM:SS D9 = HH:MM G = All other formats  (Minus) at the end = negative numbers in the cell have color setting () (brackets) at the end = this cell has the format settings with parentheses for positive or all values 
TYPE  Returns the text value corresponding to the type of content in the cell: “b” : blank or empty cell content “l” : label or text cell content “v” : number value cell content 
WIDTH  Returns the column width of the cell. The unit is the width of one zero (0) character in default font size. 
PROTECT  Returns the protection status of the cell: 1 = cell is protected 0 = cell is unprotected 
PARENTHESES  Returns 1 if the cell has the format settings with parentheses for positive or all values, otherwise returns 0 
PREFIX  Returns single character text strings corresponding to the alignment of the cell. “'” (APOSTROPHE, U+0027) = left alignment '"' (QUOTATION MARK, U+0022) = right alignment ^(caret) = centered alignment \(back slash) = filled alignment otherwise, returns empty string "". 
Summary: Returns the column number(s) of a reference
Syntax: COLUMN( [ Reference R ] )
Returns: Number
Constraints: AREAS(R) = 1
Semantics: Returns the column number of a reference, where “A” is 1, “B” is 2, and so on. If no parameter is given, the current cell is used. If a reference has multiple columns, an array of numbers is returned with all of the columns in the reference.
See also ROW 6.13.29, SHEET 6.13.31
Summary: Returns the number of columns in a given range
Syntax: COLUMNS( ReferenceArray R )
Returns: Number
Constraints: None
Semantics: Returns the number of columns in the range or array specified. The result is not dependent on the cell content in the range.
See also ROWS 6.13.30
Summary: Count the number of Numbers provided
Syntax: COUNT( { NumberSequenceList N }+ )
Returns: Number
Constraints: One or more parameters.
Semantics: Counts the numbers in the list of NumberSequences provided. Only numbers in references are counted; all other types are ignored. Errors are not propagated. It is implementationdefined what happens if 0 parameters are passed, but it should be an Error or 0.
See also COUNTA 6.13.7
Summary: Count the number of nonempty values
Syntax: COUNTA( { Any A }+ )
Returns: Number
Constraints: None.
Semantics: Counts the number of nonblank values in the list of Any sequences provided. A value is nonblank if it contains any content of any type, including an Error. In a reference, every cell that is not empty is included in the count. An empty string value ("") is not considered blank. Errors contained in a range are considered a nonblank value for purposes of the count; errors do not propagate. Constant expressions or formulas are allowed; these are evaluated and if they produce an Error value the Error value is counted as one nonblank value (and not propagated as an Error). It is implementationdefined what happens if 0 parameters are passed, but it should be an Error or 0. Any A may be a ReferenceList.
See also COUNT 6.13.6, ISBLANK 6.13.14
Summary: Count the number of blank values
Syntax: COUNTBLANK( ReferenceList R )
Returns: Number
Constraints: None.
Semantics: Counts the number of blank cells in the Reference provided. A cell is blank if the cell is empty for purposes of COUNTBLANK. If ISBLANK(R) is true, then it is blank. A cell with numeric value zero ('0') is not blank. It is implementationdefined whether or not a cell returning the empty string ("") is considered blank; because of this, there is a (potential) subtle difference between COUNTBLANK and ISBLANK.
Evaluators shall support one Reference as a parameter and may support a ReferenceList as a parameter.
See also COUNT 6.13.6, COUNTA 6.13.7, COUNTIF 6.13.9, ISBLANK 6.13.14
Summary: Count the number of cells in a range that meet a criteria.
Syntax: COUNTIF( ReferenceList R ; Criterion C )
Returns: Number
Constraints: Does not accept constant values as the reference parameter.
Semantics: Counts the number of cells in the reference range R that meet the Criterion C (4.11.8).
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also COUNT 6.13.6, COUNTA 6.13.7, COUNTBLANK 6.13.8, COUNTIFS 6.13.10, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: Count the number of cells that meet multiple criteria in multiple ranges.
Syntax: COUNTIFS( Reference R1 ; Criterion C1 [ ; Reference R2 ; Criterion C2 ]... )
Returns: Number
Constraints: Does not accept constant values as the reference parameter.
Semantics: Counts the number of cells that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.8). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; an entry is counted only if the same position in each array is the result of a Criterion match.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also AVERAGEIFS 6.18.6, COUNT 6.13.6, COUNTA 6.13.7, COUNTBLANK 6.13.8, COUNTIF 6.13.9, SUMIF 6.16.62, SUMIFS 6.16.63, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: Returns Number representing the specific Error type.
Syntax: ERROR.TYPE( Error E )
Returns: Number
Constraints: None.
Semantics: Returns a number representing what kind of Error has occurred. Note that unlike most functions, this function does not propagate Error values. Receiving a nonError value returns an Error. In particular, ERROR.TYPE(NA()) returns 7, and ERROR.TYPE applied to a nonError returns an Error.
See also NA 6.13.27
Summary: Returns formula at given reference as text
Syntax: FORMULA( Reference X )
Returns: String
Constraints: Reference X shall contain a formula
Semantics: Returns the formula in reference X as a string. The specific syntax of this returned string is implementationdefined. This function is intended to aid debugging by simplifying display of formulas in other cells. Error results of the referred formula cell are not propagated.
See also ISFORMULA 6.13.18
Summary: Returns information about the environment
Syntax: INFO( Text Category )
Returns: Any (see below)
Constraints: Category shall be valid
Semantics: Returns information about the environment in the given category.
Evaluators shall support at least the following categories:
Table 18  INFO
Category  Meaning  Type 
"directory"  Current directory. This shall be formatted so file names can be appended to the result (e.g., on POSIX and Windows systems it shall end with the separator “/” or “\” respectively).  Text 
"memavail"  Amount of memory “available”, in bytes. On many modern (virtual memory) systems this value is not really available, but a system should return 0 if it is known that there is no more memory available, and greater than 0 otherwise  Number 
"memused"  Amount of memory used, in bytes, by the data  Number 
"numfile"  Number of active worksheets in files  Number 
"osversion"  Operating system version  Text 
"origin"  The top leftmost visible cell's absolute reference prefixed with “$A:”. In locales where cells are ordered righttoleft, the top rightmost visible cell is used instead.  Text 
"recalc"  Current recalculation mode. If the locale is English, this is either "Automatic" or "Manual" (the exact text depends on the locale)  Text 
"release"  The version of the implementation.  Text 
"system"  The type of the operating system.
 Text 
"totmem"  Total memory available in bytes, including the memory already used.  Number 
Evaluators may support other categories.
See also CELL 6.13.3
Summary: Return TRUE if the referenced cell is blank, else return FALSE
Syntax: ISBLANK( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Number, Text, or Logical, return FALSE. If X is a reference to a cell, examine the cell; if it is blank (has no value), return TRUE, but if it has a value, return FALSE. A cell with the empty string is not considered blank.
See also ISNUMBER 6.13.22, ISTEXT 6.13.25
Summary: Return True if the parameter has type Error and is not NA, else return False.
Syntax: ISERR( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Error, and ISNA(X) is not true, returns TRUE. Otherwise it returns FALSE. Note that this function returns False if given NA(); if this is not desired, use ISERROR 6.13.16. Note that this function does not propagate Error values.
ISERR(X) is the same as:
IF(ISNA(X),FALSE(),ISERROR(X))
See also ERROR.TYPE 6.13.11, ISERROR 6.13.16, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27
Summary: Return TRUE if the parameter has type Error, else return FALSE
Syntax: ISERROR( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Error, returns TRUE, else returns FALSE. Note that this function returns True if given NA(); if this is not desired, use ISERR 6.13.15. Note that this function does not propagate Error values.
See also ERROR.TYPE 6.13.11, ISERR 6.13.15, ISNA 6.13.20, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27
Summary: Return TRUE if the value is even, else return FALSE
Syntax: ISEVEN( Number X )
Returns: Logical
Constraints: None
Semantics: First, compute X1=TRUNC(X). Then, if X1 is even (a division by 2 has a remainder of 0), return True, else return False. The result is implementationdefined if given a Logical value; an evaluator may return either an Error or the result of converting the Logical value to a Number (per Conversion to Number 6.3.5 ).
See also ISODD 6.13.23
Summary: Return TRUE if the reference refers to a formula, else return FALSE
Syntax: ISFORMULA( Reference X )
Returns: Logical
Constraints: None
Semantics: If X refers to a cell whose value is computed by a formula, return TRUE(), else return FALSE(). A formula itself may compute a constant; in that case it will still return TRUE() since it is still a formula. Passing a nonreference, or a reference to more than one cell, is implementationdefined.
See also ISTEXT 6.13.25, ISNUMBER 6.13.22
Summary: Return TRUE if the parameter has type Logical, else return FALSE
Syntax: ISLOGICAL( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Logical, returns TRUE, else FALSE. Evaluators that do not have a distinct Logical type will return the same value ISNUMBER(X) would return.
See also ISTEXT 6.13.25, ISNUMBER 6.13.22
Summary: Return True if the parameter is of type NA, else return False.
Syntax: ISERR( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is NA, return True, else return False. Note that if X is a reference, the value being referenced is considered. This function does not propagate Error values.
See also ERROR.TYPE 6.13.11, ISERROR 6.13.16, ISERR 6.13.15, ISNUMBER 6.13.22, ISTEXT 6.13.25, NA 6.13.27
Summary: Return TRUE if the parameter does not have type Text, else return FALSE
Syntax: ISNONTEXT( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Text, ISNONTEXT returns FALSE, else TRUE. If X is a reference, it examines what X references. References to empty cells are not considered text, so for reference to an empty cell ISNONTEXT will return TRUE. Empty Cell 4.7
ISNONTEXT(X) is equivalent to NOT(ISTEXT(X))
See also ISNUMBER 6.13.22, ISLOGICAL 6.13.19, ISTEXT 6.13.25
Summary: Return TRUE if the parameter has type Number, else return FALSE
Syntax: ISNUMBER( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Number, returns TRUE, else FALSE. Evaluators need not have a distinguished Logical type; in such evaluators, ISNUMBER(TRUE()) is TRUE.
See also ISTEXT 6.13.25, ISLOGICAL 6.13.19
Summary: Return TRUE if the value is even, else return FALSE
Syntax: ISODD( Number X )
Returns: Logical
Constraints: None
Semantics: First, compute X1=TRUNC(X). Then, if X1 is odd (a division by 2 has a remainder of 1), return True, else return False. The result is implementationdefined if given a Logical value; an evaluator may return either an Error or the result of converting the Logical value to a Number (per Conversion to Number 6.3.5 ).
See also ISEVEN 6.13.17
Summary: Return True if the parameter is of type reference, else return False.
Syntax: ISREF( Any X )
Returns: Logical
Constraints: None
Semantics: If X is of type Reference or ReferenceList, return True, else return False. Note that unlike nearly all other functions, when given a reference this function does not then examine the value being referenced. Some functions and operators return references, and thus ISREF will return True when given their results. X may be a ReferenceList, in which case ISREF returns True.
See also ISNUMBER 6.13.22, ISTEXT 6.13.25
Summary: Return TRUE if the parameter has type Text, else return FALSE.
ISTEXT(X) is equivalent to NOT(ISNONTEXT(X)).
Syntax: ISTEXT( Scalar X )
Returns: Logical
Constraints: None
Semantics: If X is of type Text, returns TRUE, else FALSE. References to empty cells are NOT considered Text. If X is a reference, examines what X references. References to empty cells are NOT considered Text, so a reference to a empty cell will return FALSE. Empty Cell 4.7
See also ISNONTEXT 6.13.21, ISNUMBER 6.13.22, ISLOGICAL 6.13.19
Summary: Return the number of a value.
Syntax: N( Any X )
Returns: Number
Constraints: None
Semantics: If X is a Reference, it is first dereferenced to a scalar. Then its type is examined. If it is of type Number, it is returned. If it is of type Logical, 1 is returned if TRUE else 0 is returned. It is implementationdefined what happens if it is provided a Text value.
See also T 6.20.22, VALUE 6.13.34
Summary: Return the constant Error value #N/A.
Syntax: NA()
Returns: Error
Constraints: Shall have 0 parameters
Semantics: This function takes no arguments and returns the Error NA
See also ERROR.TYPE 6.13.11, ISERROR 6.13.16
Summary: Convert text to number, in a localeindependent way
Syntax: NUMBERVALUE( Text X [ ; Text DecimalSeparator [ ; Text GroupSeparator ] ] )
Returns: Number
Constraints: LEN(DecimalSeparator) = 1, DecimalSeparator shall not appear in GroupSeparator
Semantics: Converts given Text value X into Number. If X is a Reference, it is first dereferenced.
X is transformed according to the following rules:
1)Starting from the beginning, remove all occurrences of the group separator before any decimal separator
2)Starting from the beginning, replace the first occurrence in the text of the decimal separator character with the FULL STOP (U+002E) character
3)Remove all whitespace characters (5.14).
4)If the first character of the resulting string is a period FULL STOP (U+002E) then prepend a zero
5)If the string ends in one or more instances of PERCENT SIGN (U+0025) , remove the percent sign(s)
If the resulting string is a valid xsd:float, then return the number corresponding to that string, according to the definition provided in XML Schema, Part 2, Section 3.2.4. If percent signs were removed in step 5, divide the value of the returned number by 100 for each percent sign removed.
If the string is not a valid xsd:float then return an error.
See also N 6.13.26, T 6.20.22, DATEVALUE 6.10.4, TIMEVALUE 6.10.18, VALUE 6.13.34
Summary: Returns the row number(s) of a reference
Syntax: ROW( [ Reference R ] )
Returns: Number
Constraints: AREAS(R) = 1
Semantics: Returns the row number of a reference. If no parameter is given, the current cell is used. If a reference has multiple rows, an array of numbers is returned with all of the rows in the reference.
See also COLUMN 6.13.4, SHEET 6.13.31
Summary: Returns the number of rows in a given range
Syntax: ROWS( ReferenceArray R )
Returns: Number
Constraints: None
Semantics: Returns the number of rows in the range or array specified. The result is not dependent on the cell content in the range.
See also COLUMNS 6.13.5
Summary: Returns the sheet number of the reference or the string representing a sheet name.
Syntax: SHEET( [ TextReference R ] )
Returns: Number >= 1
Constraints: R shall not contain a Source Location (5.8 References)
Semantics: Returns the 1 based sheet number of the given reference or sheet name.
Hidden sheets are not excluded from the sheet count.
If no parameter is given, the result is the sheet number of the sheet containing the formula.
If a Reference is given it is not dereferenced.
If the reference encompasses more than one sheet, the result is the number of the first sheet in the range.
If a reference does not contain a sheet reference, the result is the sheet number of the sheet containing the formula.
If the function is not evaluated within a table cell, an error is returned.
See also COLUMN 6.13.4, ROW 6.13.29, SHEETS 6.13.32
Summary: Returns the number of sheets in a reference or current document
Syntax: SHEETS( [ Reference R ] )
Returns: Number >= 1
Constraints: R shall not contain a Source Location (5.8 References)
Semantics: Returns the number of sheets in the given reference.
If no parameter is given, the number of sheets in the document is returned.
Hidden sheets are not excluded from the sheet count.
See also COLUMNS 6.13.5, ROWS 6.13.30, SHEET 6.13.31
Summary: Returns a number indicating the type of the provided value.
Syntax: TYPE( Any value )
Returns: Number
Constraints: None
Semantics: Returns a number indicating the type of the value given:
Table 19  TYPE
Value's Type  TYPE Return 
Number  1 
Text  2 
Logical  4 
Error  16 
Array  64 
If a Reference is provided, the reference is first dereferenced, and any formulas are evaluated.
Note: Reliance on the return of 4 for TYPE() will impair the interoperability of a document containing an expression that relies on that value.
See also ERROR.TYPE 6.13.11
Summary: Convert text to number
Syntax: VALUE( Text X )
Returns: Number
Constraints: None
Semantics: Converts given text value X into Number. If X is a Reference, it is first dereferenced. VALUE is only specified if it is given a Text value or a Reference to a single cell containing a Text value; it is implementationdefined what happens if VALUE is given neither a Text value nor a Reference to a Text value. If the Text has a date, time, or datetime format, it is converted into a serial Number. In many cases the conversion of a date or datetime format is localedependent.
If the supplied text X cannot be converted into a Number, an Error is returned.
Regardless of the current locale, an evaluator shall accept numbers matching this regular expression (which does not include a decimal point character) and convert it into a Number. If the value ends in %, it shall divide the number by 100:
[+]? [09]+([eE][+]?[09]+)?)%?
VALUE shall accept text representations of numbers in the current locale. In the en_US locale, an evaluator shall accept decimal numbers matching this regular expression and convert it into a Number (the leading “$” is ignored; commas are ignored if they match the rule of a thousands separator; if the value ends in %, it shall divide the number by 100):
[+]?\$?([09]+(,[09]{3})*)?(\.[09]+)?(([eE][+]?[09]+)%)?
Evaluators shall accept accept fractional values matching the regular expression:
[+]? [09]+ \ [09]+/[19][09]?
A leading minus sign is considered identifying a negative number for the entire value. There is a space between the integer and the fractional portion; values between 0 and 1 can be represented by using 0 for the integer part.
Evaluators shall support time values in at least the HH:MM and HH:MM:SS formats, where HH is a 12 digit value from 0 to 23, MM is a 12 digit value from 0 to 59, and SS is a 12 digit value from 0 to 59. The hour may be one or two digits when it is less than 10. VALUE converts time values into Numbers ranging from 0 to 1, which is percentage of day that has elapsed by that time. Thus, VALUE("2:00") is the same as 2/24. Evaluators should accept times with fractional seconds as well when expressed in the form HH:MM:SS.ssss...
Evaluators shall accept textual dates in [ISO8601] format (YYYYMMDD), converting them into serial numbers based on the current epoch. Evaluators shall, when running in the en_US locale, accept the format MM/DD/YYYY .
In addition, in locale en_US, evaluators shall support the following formats (where YYYY is a 4digit year, YY a 2digit year, MM a numerical month, DD a numerical day, mmm a 3character abbreviated alphabetical name, and mmmmm a full name):
Table 20  VALUE
Format  Example  Comment 
MM/DD/YYYY  5/21/2006  LOCALEDEPENDENT; Long year format with slashes. 
MM/DD/YY  5/21/06  LOCALEDEPENDENT; Short year format with slashes 
MMDDYYYY  5212006  LOCALEDEPENDENT; Long year format with dashes (short year may be supported, but it may also be used for years less than 100 . 
mmm DD, YYYY  Oct 29, 2006  LOCALEDEPENDENT; Short alphabetic month day, year. Note: mmm depends on the locale's language. 
DD mmm YYYY  29 Oct 2006  LOCALEDEPENDENT; Short alphabetic day month year 
mmmmm DD, YYYY  October 29, 2006  LOCALEDEPENDENT; Long alphabetic month day, year 
DD mmmmm YYYY  29 October 2006  LOCALEDEPENDENT; Long alphabetic day month year 
Evaluators should support other locales. Many conversions will vary by locale, including the decimal point (comma or period), names of months, date formats (MM/DD vs. DD/MM), and so on. Dates in particular vary by locale.
Evaluators shall support the datetime format, which is a date followed by a time, using either the space character or the literal “T” character as the separator (the “T” is from ISO 8601). Evaluators shall support at least the ISO date format in a datetime format; they may support other date formats in a datetime format as well. Formats such as “YYYYMMDD HH:MM” and “YYYYMMDDTHH:MM:SS” (where “T” is the literal character T) shall be accepted. The result of accepting a datetime format shall be a representation of that specific time (without removing either the date or the time of day, unlike DATEVALUE or TIMEVALUE).
Evaluators may accept other formats that will convert to numbers, and those conversions may be localedependent, as long as they do not conflict with the above. Where no conversion is determined, an Error is returned.
See also N 6.13.26, T 6.20.22, DATEVALUE 6.10.4, TIMEVALUE 6.10.18, NUMBERVALUE 6.13.28
These functions look up information. Note that IF() can be considered a trivial lookup function, but it is listed as a logical function instead.
Summary: Returns a cell address (reference) as text
Syntax: ADDRESS( Integer Row ; Integer Column [ ; Integer Abs = 1 [ ; Logical A1 = TRUE() [ ; Text Sheet ] ] ] )
Returns: Text
Constraints: Row >= 1, Column >= 1, 1 <= Abs <= 4; A1 = TRUE(). Evaluators may evaluate expressions that do not meet the constraint A1 = TRUE().
Semantics: Returns a cell address (reference) as text. The text does not include the surrounding [...] of a reference. If a Sheet name is given, the sheet name in the text returned is followed by a “.” and the column/row reference if A1 is TRUE, or a “!” and the column/row reference if A1 is FALSE; otherwise no “.” respectively “!” is included. Columns are identified using uppercase letters. The value of Abs determines if the column and/or row is absolute or relative. The value of A1 determines if A1 reference style or R1C1 reference style is used.
Table 21  ADDRESS
Abs  Meaning  A1 = TRUE()  A1 = FALSE() 
1  fully absolute  $A$1  R1C1 
2  row absolute, column relative  A$1  R1C[1] 
3  row relative, column absolute  $A1  R[1]C1 
4  fully relative  A1  R[1]C[1] 
Note that the INDIRECT function accepts this format.
See also INDIRECT 6.14.7
Summary: Uses an index to return a value from a list of values.
Syntax: CHOOSE( Integer Index ; { Any Value }+ )
Returns: Any
Constraints: Returns an Error if Index < 1 or if there is no corresponding value in the list of Values.
Semantics: Uses Index to determine which value, from a list of values, to return. If Index is 1, CHOOSE returns the first Value; if Index is 2, CHOOSE returns the second value, and so on. Note that the Values may be formula expressions. Expression paths of parameters other than the one chosen are not calculated or evaluated for side effects.
See also IF 6.15.4
Summary: Return a value from a data pilot table.
Syntax: GETPIVOTDATA( Text DataField ; Reference Table { ; Text Field ; Scalar Member }* )
Note: This function knows two different syntaxes. This version of the syntax is distinguished by the second parameter Table being a Reference.
Returns: Any
Semantics: Returns a single result from the calculation of a data pilot table.
The data pilot table is selected by Table, which is a reference to a cell or cell range that's within a data pilot table or contains a data pilot table. If the cell range contains several data pilot tables, the last one in the order of <table:datapilottable> elements in the file is used.
DataField selects one of the data pilot table's data fields. It can be the name of the source column, or the given name of the data field (such as “Sum of Sales”).
If no Field/Member pairs are given, the grand total is returned. Otherwise, each pair adds a constraint that the result shall satisfy. Field is the name of a field from the data pilot table. Member is the name of a member (item) from that field. If a member is a number, Member can alternatively be its numerical value.
If the data pilot table contains only a single result value that fulfills all of the constraints, or a subtotal result that summarizes all matching values, that result is returned. If there is no matching result, or several ones without a subtotal for them, an Error is returned. These conditions apply to results that are included in the data pilot table. If the source data contains entries that are hidden by settings of the data pilot table, they are ignored. The order of the Field/Member pairs is not significant. Field and member names are caseinsensitive.
If no constraint for a page field is given, the field's selected value is implicitly used. If a constraint for a page field is given, it shall match the field's selected value, or an Error is returned.
Subtotal values from the data pilot table are only used if they use the function “auto” (except when specified in the constraint, see below).
Alternative syntax: GETPIVOTDATA( Reference Table ; Text Constraints )
For compatibility, a second syntax is allowed. Table has the same meaning as above. This version of the syntax is distinguished by the first parameter Table being a Reference.
Constraints is a spaceseparated list. Entries can be quoted (single quotes). One of the entries can be the data field name. The data field name can be left out if the data pilot table contains only one data field, otherwise it shall be present. Each of the other entries specifies a constraint in the form Field[Member] (with literal characters [ and ]), or only Member if the member name is unique within all fields that are used in the data pilot table. A function name can be added in the form Field[Member;Function], which will cause the constraint to match only subtotal values which use that function. The possible function names are the same as in the table:function attribute of the <table:datapilotsubtotal> element, caseinsensitive.
Summary: Look for a matching value in the first row of the given table, and return the value of the indicated row.
Syntax: HLOOKUP( Any Lookup ; ReferenceArray DataSource ; Integer Row [ ; Logical RangeLookup = TRUE() ] )
Returns: Any
Constraints: Row >= 1; Searched portion of DataSource shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a DataSource not include Logical values.
Semantics:
If RangeLookup is omitted or TRUE or not 0, the first row of DataSource is assumed to be sorted in ascending order, with smaller numbers before larger ones, smaller text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. The lookup will try to match an entry of value Lookup. If none is found the largest entry less than Lookup is taken as a match. From a sequence of identical values <= Lookup the last entry is taken. If there is no data less than or equal to Lookup, the #N/A Error is returned. If Lookup is of type Text and the value found is of type Number, the #N/A Error is returned. If DataSource is not sorted, the result is undetermined and implementationdependent. In most cases it will be arbitrary and just plain wrong due to binary search algorithms.
If RangeLookup is FALSE or 0, DataSource does not need to be sorted and an exact match is searched. Each value in the first row of DataSource is examined in order (starting at the left) until its value matches Lookup.
Both methods, if there is a match, return the corresponding value in row Row, relative to the DataSource, where the topmost row in DataSource is 1.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11, VLOOKUP 6.14.12
Summary: Returns a value using a row and column index value (and optionally an area index).
Syntax: INDEX( ReferenceListArray DataSource ; [ Integer Row ] [ ; [ Integer Column ] ] [ ; Integer AreaNumber = 1 ] )
Returns: Any
Constraints: Row >= 0, Column >= 0,
1 <= AreaNumber <= number of references in DataSource if that is a ReferenceList, else AreaNumber = 1
Semantics:
Given a DataSource, returns the value at the given Row and Column (starting numbering at 1, relative to the top left of the DataSource) of the given area AreaNumber. If AreaNumber is not given, it defaults to 1 (the first and possibly only area). This function is essentially a twodimensional version of CHOOSE, which does not accept range parameters.
If Row is omitted or an empty parameter (two consecutive ;; semicolons) or 0, an entire column of the given area AreaNumber in DataSource is returned. If Column is omitted or an empty parameter (two consecutive ;; semicolons) or 0, an entire row of the given area AreaNumber in DataSource is returned. If both, Row and Column, are omitted or empty or 0, the entire given area AreaNumber is returned.
If DataSource is a onedimensional column vector, Column is optional or can be omitted as an empty parameter (two consecutive ;; semicolons). If DataSource is a onedimensional row vector, Row is optional, which effectively makes Row act as the column offset into the vector, or can be omitted as an empty parameter (two consecutive ;; semicolons).
If Row or Column have a value greater than the dimension of the corresponding given area AreaNumber, an Error is returned.
See also AREAS 6.13.2, CHOOSE 6.14.3
Summary: Return a reference given a string representation of a reference
Syntax: INDIRECT( Text Ref [ ; Logical A1 = TRUE() ] )
Returns: Reference
Constraints: Ref is valid reference
Semantics: Given text for a reference (such as “A3”), returns a reference. If A1 is False, it is interpreted as an R1C1 reference style. For interoperability, if the Ref text includes a sheet name, evaluators should be able to parse both, the “.” dot and the “!” exclamation mark, as the sheet name separator. If evaluators support the A1=FALSE() case of the ADDRESS 6.14.2 function and include the “!” exclamation mark as the sheet name separator, evaluators shall correctly parse that in the A1=FALSE() case of this INDIRECT function. Evaluators shall correctly parse the “.” dot as the sheet name separator in the A1=TRUE() case.
See also ADDRESS 6.14.2
Summary: Look for criterion in an alreadysorted array, and return a corresponding result
Syntax: LOOKUP( Any Find ; ForceArray ReferenceArray Searched [ ; ForceArray ReferenceArray Results ] )
Returns: Any
Constraints: The searched portion of Searched shall be sorted in ascending order; if provided, Results shall have the same length as Searched. The searched portion of Searched shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a Searched not include Logical values.
Semantics: This function searches for Find in a row or column of the previouslysorted array Searched and returns a corresponding value. The match is the largest value in the row/column of Searched that is less than or equal to Find (so an exact match is always preferred over inexact ones). From a sequence of identical values <= Find the last entry is taken. If Find is smaller than the smallest value in the first row or column (depending on the array dimensions), LOOKUP returns the #N/A Error. If Find is of type Text and the value found is of type Number, the #N/A Error is returned.
The searched portion of Searched shall be sorted in ascending order, and so that values of type Number precede values of type Text if both types are included (e.g., 2, 0, 2, “A”, “B”).
There are two major uses for this function; the 3parameter version (vector) and the 2parameter version (nonvector array).
Note: Interoperability is improved by use of HLOOKUP or VLOOKUP in expressions over LOOKUP.
When given two parameters, Searched is first examined:
When given 3 parameters, Results shall be a vector (either a row or a column) or an Error is raised. The function determines the index of the match in the first column respectively row of Searched, and returns the value in Results with the same index.
Searched is first examined:
The lengths of the search vector and the result vector do not need to be identical. When the match position falls outside the length of the result vector, an Error is returned if the result vector is given as an array object. If it is a cell range, it gets automatically extended to the length of the searched vector, but in the direction of the result vector. If just a single cell reference was passed, a column vector is generated. If the cell range cannot be extended due to the sheet's size limit, then the #N/A Error is returned.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also HLOOKUP 6.14.5, INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11, VLOOKUP 6.14.12
Summary: Finds a Search item in a sequence, and returns its position (starting from 1).
Syntax: MATCH( Scalar Search ; ReferenceArray SearchRegion [ ; Integer MatchType = 1 ] )
Returns: Any
Constraints: 1 <= MatchType <= 1; The searched portion of SearchRegion shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a SearchRegion not include Logical values.
SearchRegion shall be a vector (a single row or column)
Semantics:
If a match is found, MATCH returns the relative position (starting from 1). For Text the comparison is caseinsensitive. MatchType determines the type of search; if MatchType is 0, the SearchRegion shall be considered unsorted, and the first match is returned. If MatchType is 1, the SearchRegion may be assumed to be sorted in ascending order, with smaller Numbers before larger ones, smaller Text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. If MatchType is 1, then SearchRegion may be assumed to be sorted in descending order (the opposite of the above). If MatchType is 1 or 1, evaluators may use binary search or other techniques so that they do not need to examine every value in linear order. MatchType defaults to 1.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also HLOOKUP 6.14.5, OFFSET 6.14.11, VLOOKUP 6.14.12
Summary: Executes a formula expression while substituting a row reference and a column reference.
Syntax: MULTIPLE.OPERATIONS( Reference FormulaCell ; Reference RowCell ; Reference RowReplacement [ ; Reference ColumnCell ; Reference ColumnReplacement ] )
Returns: Any
Semantics:
MULTIPLE.OPERATIONS executes the formula expression pointed to by FormulaCell and all formula expressions it depends on while replacing all references to RowCell with references to RowReplacement respectively all references to ColumnCell with references to ColumnReplacement.
If calls to MULTIPLE.OPERATIONS are encountered in dependencies, replacements of target cells shall occur in queued order, with each replacement using the result of the previous replacement.
Note: The function may be used to create tables of expressions that depend on two input parameters.
Example: FormulaCell is B5, RowCell is B3, ColumnCell is B2
Table 22  MULTIPLE.OPERATIONS
 col_B  col_C  col_D  col_E  col_F 
row_2  1   1  2  3 
row_3  1  1  =MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;D$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;E$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C3;$B$2;F$2) 
row_4  =B2+B3  2  =MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;D$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;E$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C4;$B$2;F$2) 
row_5  =B2*B3+B4  3  =MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;D$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;E$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C5;$B$2;F$2) 
  4  =MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;D$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;E$2)  =MULTIPLE.OPERATIONS($B$5;$B$3;$C6;$B$2;F$2) 
Result:
Table 23  MULTIPLE.OPERATIONS
 col_B  col_C  col_D  col_E  col_F 
row_2  1   1  2  3 
row_3  1  1  3  5  7 
row_4  2  2  5  8  11 
row_5  3  3  7  11  15 
  4  9  14  19 
Note that although only cell B5 is passed as the FormulaCell parameter, also the references to B2 and B3 of the formula in cell B4 are replaced, because B5 depends on B4.
Summary: Modifies a reference's position and dimension.
Syntax: OFFSET( Reference reference ; Integer rowOffset ; Integer columnOffset [ ; [ Integer newHeight ] [ ; [ Integer newWidth ] ] ] )
Returns: Reference
Constraints: newWidth > 0; newHeight > 0
The modified reference shall be in a valid range, starting from column/row one to the maximum column/row.
Semantics: Shifts reference by rowOffset rows and by columnOffset columns. Optionally, the dimension can be set to newWidth and/or newHeight, if omitted the width/height of the original reference is taken. Note that newHeight may be empty (two consecutive semicolons ;;) followed by a given newWidth argument. Returns the modified reference.
See also COLUMN 6.13.4, COLUMNS 6.13.5, ROW 6.13.29, ROWS 6.13.30
Summary: Look for a matching value in the first column of the given table, and return the value of the indicated column.
Syntax: VLOOKUP( Any Lookup ; ReferenceArray DataSource ; Integer Column [ ; Logical RangeLookup = TRUE() ] )
Returns: Any
Constraints: Column >= 1; The searched portion of DataSource shall not include Logical values. Evaluators may evaluate expressions that do not meet the constraint that the searched portion of a DataSource not include Logical values.
Semantics:
If RangeLookup is omitted or TRUE or not 0, the first column of DataSource is assumed to be sorted in ascending order, with smaller Numbers before larger ones, smaller Text values before larger ones (e.g., "A" before "B", and "B" before "BA"), and False before True. If the types are mixed, Numbers are sorted before Text, and Text before Logicals; evaluators without a separate Logical type may include a Logical as a Number. The lookup will try to match an entry of value Lookup. From a sequence of identical values <= Lookup the last entry is taken. If none is found the largest entry less than Lookup is taken as a match. If there is no data less than or equal to Lookup, the #N/A Error is returned. If Lookup is of type Text and the value found is of type Number, the #N/A Error is returned. If DataSource is not sorted, the result is undetermined and implementationdependent. In most cases it will be arbitrary and just plain wrong due to binary search algorithms.
If RangeLookup is FALSE or 0, DataSource does not need to be sorted and an exact match is searched. Each value in the first column of DataSource is examined in order (starting at the top) until its value matches Lookup. If no value matches, the #N/A Error is returned.
Both methods, if there is a match, return the corresponding value in column Column, relative to the DataSource, where the leftmost column in DataSource is 1.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also HLOOKUP 6.14.5, INDEX 6.14.6, MATCH 6.14.9, OFFSET 6.14.11
The logical functions are the constants TRUE() and FALSE(), the functions that compute Logical values NOT(), AND(), and OR(), and the conditional function IF(). The OpenDocument specification mentions "logical operators"; these are another name for the logical functions.
Note that because of Error values, any logical function that accepts parameters can actually produce TRUE, FALSE, or an Error value, instead of TRUE or FALSE.
These are not bitwise operations, e.g., AND(12;10) produces TRUE(), not 8. See the bit operation functions for bitwise operations.
Summary: Compute logical AND of all parameters.
Syntax: AND( { LogicalNumberSequenceList L }+ )
Returns: Logical
Constraints: Shall have 1 or more parameters
Semantics: Computes the logical AND of the parameters. If all parameters are True, returns True; if any are False, returns False. When given one parameter, this has the effect of converting that one parameter into a Logical value. When given zero parameters, evaluators may return a Logical value or an Error.
Also in array context a logical AND of all arguments is computed, range or array parameters are not evaluated as a matrix and no array is returned. This behavior is consistent with functions like SUM. To compute a logical AND of arrays per element use the * operator in array context.
See also OR 6.15.8, IF 6.15.4
Summary: Returns constant FALSE
Syntax: FALSE()
Returns: Logical
Constraints: Shall have 0 parameters
Semantics: Returns logical constant FALSE. This may be a Number or a distinct type.
See also TRUE 6.15.9, IF 6.15.4
Summary: Return one of two values, depending on a condition
Syntax: IF( Logical Condition [ ; [ Any IfTrue ] [ ; [ Any IfFalse ] ] ] )
Returns: Any
Constraints: None.
Semantics: Computes Condition. If it is TRUE, it returns IfTrue, else it returns IfFalse. If there is only 1 parameter, IfTrue is considered to be TRUE(). If there are less than 3 parameters, IfFalse is considered to be FALSE(). Thus the 1 parameter version converts Condition into a Logical value. If there are 2 or 3 parameters but the second parameter is null (two consecutive ;; semicolons), IfFalse is considered to be 0. If there are 3 parameters but the third parameter is null, IfFalse is considered to be 0. This function only evaluates IfTrue, or ifFalse, and never both; that is to say, it shortcircuits.
See also AND 6.15.2, OR 6.15.8
Summary: Return X unless it is an Error, in which case return an alternative value
Syntax: IFERROR( Any X ; Any Alternative )
Returns: Any
Constraints: None.
Semantics: Computes X. If ISERROR(X) is true, return Alternative, else return X.
Note: This is semantically equivalent to IF(ISERROR(X); Alternative; X), except that X is only computed once.
See also IF 6.15.4, ISERROR 6.13.16
Summary: Return X unless it is an NA, in which case return an alternative value
Syntax: IFNA( Any X ; Any Alternative )
Returns: Any
Constraints: None.
Semantics: Computes X. If ISNA(X) is true, return Alternative, else return X.
Note: This is semantically equivalent to IF(ISNA(X); Alternative; X), except that X is only computed once.
See also IF 6.15.4, ISNA 6.13.20
Summary: Compute logical NOT
Syntax: NOT( Logical L )
Returns: Logical
Constraints: Shall have 1 parameter
Semantics: Computes the logical NOT. If given TRUE, returns FALSE; if given FALSE, returns TRUE.
See also AND 6.15.2, IF 6.15.4
Summary: Compute logical OR of all parameters.
Syntax: OR( { LogicalNumberSequenceList L }+ )
Returns: Logical
Constraints: Shall have 1 or more parameters
Semantics: Computes the logical OR of the parameters. If all parameters are False, it shall return False; if any are True, it shall returns True. When given one parameter, this has the effect of converting that one parameter into a Logical value. When given zero parameters, evaluators may return a Logical value or an Error.
Also in array context a logical OR of all arguments is computed, range or array parameters are not evaluated as a matrix and no array is returned. This behavior is consistent with functions like SUM. To compute a logical OR of arrays per element use the + operator in array context.
See also AND 6.15.2, IF 6.15.4
Summary: Returns constant TRUE
Syntax: TRUE()
Returns: Logical
Constraints: Shall have 0 parameters
Semantics: Returns logical constant TRUE. The result of this function may but need not be equal to 1 when compared using “=”. It always has the value of 1 if used in a context requiring Number (because of the automatic conversions), so if ISNUMBER(TRUE()), then it shall have the value 1.
See also FALSE 6.15.3, IF 6.15.4
Summary: Compute a logical XOR of all parameters.
Syntax: XOR( { Logical L }+ )
Returns: Logical
Constraints: Shall have 1 or more parameters.
Semantics: Computes the logical XOR of the parameters such that the result is an addition modulo 2. If an even number of parameters is True it returns False, if an odd number of parameters is True it returns True. When given one parameter, this has the effect of converting that one parameter into a Logical value.
See also AND 6.15.2, OR 6.15.8
This section describes functions for various mathematical functions, including trigonometric functions like SIN 6.16.55). Note that the constraint text presumes that a value of type Number is a real number (no imaginary component). Unless noted otherwise, all angle measurements are in radians.
Summary: Return the absolute (nonnegative) value.
Syntax: ABS( Number N )
Returns: Number
Constraints: None
Semantics: If N < 0, returns N, otherwise returns N.
See also Prefix Operator “” 6.4.16
Summary: Returns the principal value of the arc cosine of a number. The angle is returned in radians.
Syntax: ACOS( Number N )
Returns: Number
Constraints: 1.0 <= N <= 1.0.
Semantics: Computes the arc cosine of a number, in radians.
Returns a principal value 0 ≤ result ≤ PI.
See also COS 6.16.19, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the principal value of the inverse hyperbolic cosine
Syntax: ACOSH( Number N )
Returns: Number
Constraints: N >= 1
Semantics: Computes the principal value of the inverse hyperbolic cosine.
See also COSH 6.16.20, ASINH 6.16.8
Summary: Return the principal value of the arc cotangent of a number. The angle is returned in radians.
Syntax: ACOT( Number N )
Returns: Number
Semantics: Computes the arc cotangent of a number, in radians.
Returns a principal value 0 < result < PI.
See also COT 6.16.21, ATAN 6.16.9, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the hyperbolic arc cotangent
Syntax: ACOTH( Number N )
Returns: Number
Constraints: ABS(N) > 1
Semantics: Computes the hyperbolic arc cotangent. The hyperbolic arc cotangent is an analog of the ordinary (circular) arc cotangent.
See also COSH 6.16.20, ASINH 6.16.8
Summary: Return the principal value of the arc sine of a number. The angle is returned in radians.
Syntax: ASIN( Number N )
Returns: Number
Constraints: 1 <= N <= 1.
Semantics: Computes the arc sine of a number, in radians.
Returns a principal value PI/2 ≤ result ≤ PI/2.
See also SIN 6.16.55, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the principal value of the inverse hyperbolic sine
Syntax: ASINH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the principal value of the inverse hyperbolic sine.
See also SINH 6.16.56, ACOSH 6.16.4
Summary: Return the principal value of the arc tangent of a number. The angle is returned in radians.
Syntax: ATAN( Number N )
Returns: Number
Semantics: Computes the arc tangent of a number, in radians.
Returns a principal value PI/2 < result < PI/2.
See also ATAN2 6.16.10, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Returns the principal value of the arc tangent given a coordinate of two numbers.
The angle is returned in radians.
Syntax: ATAN2( Number x ; Number y )
Returns: Number
Constraints: x<>0 or y<>0
Semantics: Computes the arc tangent of two numbers (the x and y coordinates of a point), in radians. This is similar to ATAN(y/x), but the signs of the two numbers are taken into account so that the result covers the full range from PI() to +PI(). ATAN2(0;0) is implementationdefined, evaluators may return 0 or an Error.
Returns a principal value PI < result ≤ PI.
See also ATAN 6.16.9, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the principal value of the inverse hyperbolic tangent
Syntax: ATANH( Number N )
Returns: Number
Constraints: 1 < N < 1
Semantics: Computes the principal value of the inverse hyperbolic tangent.
See also COSH 6.16.20, SINH 6.16.56, ASINH 6.16.8, ACOSH 6.16.4, ATAN 6.16.9, ATAN2 6.16.10, FISHER 6.18.26
Summary: Returns the modified Bessel function of integer order In(x).
Syntax: BESSELI( Integer X ; Number N )
Returns: Number
Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a nonerror value.
Semantics: Computes the modified Bessel function of integer order In(x). N is also known as the order.
See also BESSELJ 6.16.13, BESSELK 6.16.14, BESSELY 6.16.15
Summary: Returns the Bessel function of integer order Jn(x) (cylinder function)
Syntax: BESSELJ( Integer X ; Number N )
Returns: Number
Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a nonerror value.
Semantics: Computes the Bessel function of integer order Jn(x). N is also known as the order.
See also BESSELI 6.16.12, BESSELK 6.16.14, BESSELY 6.16.15
Summary: Returns the modified Bessel function of integer order Kn(x).
Syntax: BESSELK( Integer X ; Number N )
Returns: Number
Constraints: N >= 0, INT (N)=N; Evaluators may evaluate expressions where N >= 0 returns a nonerror value.
Semantics: Computes the Bessel function of integer order Kn(x). N is also known as the order.
See also BESSELI 6.16.12, BESSELJ 6.16.13, BESSELY 6.16.15
Summary: Returns the Bessel function of integer order Yn(x), also known as the Neumann function.
Syntax: BESSELY( Integer X ; Number N )
Returns: Number
Constraints: N >= 0, INT(N)=N; Evaluators may evaluate expressions where N >= 0 returns a nonerror value.
Semantics: Computes Bessel function of integer order Yn(x), also known as the Neumann function. N is also known as the order.
See also BESSELI 6.16.12, BESSELJ 6.16.13, BESSELK 6.16.14
Summary: Returns the number of different Rlength sets that can be selected from N items.
Syntax: COMBIN( Integer N ; Integer R )
Returns: Number
Constraints: N >= 0, R >= 0, R <= N
Semantics: COMBIN returns the binomial coefficient, which is the number of different Rlength sets that can be selected from N items. Since they are sets, order in the sets is not relevant. The parameters are truncated (using INT) before use. For example, if a jar contains five marbles, each one a distinct color, the number of different threemarble groups COMBIN(5;3) = 10. The result is
Note that if order is important, use PERMUT instead.
See also PERMUT 6.18.59
Summary: Returns the number of combinations with repetitions.
Syntax: COMBINA( Integer N ; Integer M )
Returns: Number
Constraints: N >= 0, M >= 0, N >= M; Evaluators may evaluate expressions where N >= 0, M >= 0 returns a nonerror value.
Semantics: Returns the number of possible combinations of M objects out of N possible ones, with repetitions allowed. Actual arguments that are not integers are truncated (using INT) before use. The result is
See also COMBIN 6.16.16
Summary: Returns a number converted from one unit system into another
Syntax: CONVERT( Number N ; Text From ; Text Into )
Returns: Number
Constraints: From and Into shall be legal units, and shall be in the same unit group.
Semantics: Returns the number converted from the unit identified by From into the unit identified by Into. A unit is a unit symbol , optionally preceded by a unit prefix (either a decimal prefix or a binary prefix). Units (including both the unit symbol and the optional unit prefix) are casesensitive.
Evaluators claiming to implement this function shall support at least the following unit symbols (with conversions between them and other units in the same group):
Table 24  Unit names
Unit group  Unit symbol  Description 
Area  "uk_acre"  International acre (using international feet), exactly 4046.8564224 m2; normally not used for U.S. land areas  "us_acre"  U.S. survey/statute acre (using U.S. survey/statute feet), exactly 4046+13525426/15499969 m 2  "ang2" or "ang^2" *  Square angstrom (an Angstrom is exactly 1010 m)  "ar" *  are, 100 m2 (not abbreviated as “a”)  "ft2" or "ft^2"  Square international feet (1 foot is exactly 0.3048 m)  "ha"  hectare, 10 000 m2  "in2" or "in^2"  Square international inches (1 inch is exactly 2.54 cm)  "ly2" or "ly^2"  Square lightyear (where year=365.25 days)  "m2" or "m^2" *  Square meters  "Morgen"  Morgen, 2500 m2  "mi2" or "mi^2"  Square international miles  "Nmi2" or "Nmi^2"  Square nautical miles (1 nautical mile is 1852 m)  "Pica2" or "Pica^2" "picapt2" or "picapt^2"  Square Pica Point (one Pica point is 1/72 inch)  “pica2” or “pica^2”  Square Pica (one Pica is 1/6 inch)  "yd2" or "yd^2"  Square international yards (1 yard is 0.9144 m) 


 
Distance (Length)  "ang" *  Angstrom, exactly 1010 m  "ell"  Ell, exactly 45 international inches  "ft"  International Foot, exactly 0.3048 m and also exactly 12 international inches.  "in"  International Inch, exactly 2.54 cm.  "ly" *  Lightyear, (299792458 m/s) (3600 s/hr) (24 hr/day) (365.25 day)  "m" *  Meter  "mi"  International Mile, exactly 1609.344 m and exactly 5280 international feet. This is not a U.S. survey/statute mile (see “smi”) nor a nautical mile (see “Nmi”), but this is the mile normally used in the U.S. customary system  "Nmi"  International nautical mile, exactly 1852 m. Note that this is not the obsolete U.S. nautical mile nor the Admiralty mile.  "parsec" or "pc" *  Distance from sun to a point having heliocentric parallax of one second (used for stellar distance), AU/tan(1/3600 degree) where an AU is exactly 149,597,870.691 kilometers. *  "Pica" or "picapt"  Pica (1/72 inch)  “pica”  Pica (1/6 inch)  "survey_mi"  U.S. survey "mile, aka U.S. statute mile, exactly 6336000/3937 m; used in some U.S. maps. This is not the mile (see “mi”) normally used in the U.S.  "yd"  International yard, exactly 0.9144 m and exactly 3 international feet. 


 
Energy  "BTU" ("btu")  International Table British Thermal Unit  "c" *  Thermodynamic calorie, 4.184 J. This is not a dietary Calorie (kilocalorie). For high accuracy, use Joule, due to the many conflicting definitions of calorie.  "cal" *  International Table (IT) calorie, 4.1868 J. This is not a dietary Calorie (kilocalorie). For high accuracy, use Joule, due to the many conflicting definitions of calorie.  "e" *  Erg  "eV" ("ev") *  Electron volt (eV preferred)  "flb"  Footpound (international foot, avoirdupois pound)  "HPh" ("hh")  Horsepowerhour (HPh preferred)  "J" *  Joule  "Wh" ("wh") *  Watthour 


 
Force (Weight)  "dyn" ("dy") *  Dyne  "N" *  Newton  "lbf"  Pound force (see “lbm” for pound mass)  "pond" *  Pond, gravitational force on a mass of one gram, 9.80665E3 N. 


 
Information  "bit" * †  bit  "byte" * †  byte = 8 bits 


 
Magnetic Flux Density  

 
Mass  "g" *  Gram  "grain"  Grain, 1/7000 international pound mass (avoirdupois) (U.S. usage).  "cwt" ("shweight")  U.S. (short) hundredweight, 100 lbm  "uk_cwt" or "lcwt" ("hweight")  Imperial hundredweight, aka long hundredweight; 112 lbm  "lbm"  International pound mass (avoirdupois), exactly 453.59237 g (see “lbf” for pound force)  "stone"  14 international pound mass (avoirdupois)  "ton"  2000 international pound mass (avoirdupois) (U.S. usage). Note that there are many other measures also called “ton”; in particular, this is not a metric ton (tonne).  "ozm"  Ounce mass (avoirdupois), exactly 1/16 of an international pound mass (avoirdupois) (see “oz” for fluid ounce)  "sg"  Slug; 32.174 international pound mass (avoirdupois)  "u" *  U (atomic mass unit)  "uk_ton" or "LTON" ("brton")  Imperial ton, aka “long ton”, "deadweight ton", or "weight ton". 2240 lbm. 


 
Power  "HP" ("h")  Mechanical horsepower aka Imperial horsepower. 550 footpounds per second. The unit “h” is deprecated and should be replaced with “HP”.  "PS"  Pferdestärke (German “horse strength”, close but not identical to “HP”), the amount of power to lift a mass of 75 kilograms in one second against the earth gravitation between a distance of one meter, approximately 735.49875 W.  "W" ("w") *  Watt 


 
Pressure  "atm" ("at") *  Atmosphere  "mmHg" *  mm of Mercury  "Pa" *  Pascal; Pa preferred, as it is the standard abbreviation. Note that “P” or “p” need not be accepted.  "psi"  Pounds per square inch, using avoirdupois pounds and international inches.  "Torr"  Torr, exactly 101325/760 Pa (this is close but not equal to mmHg) 


 
Speed  "admkn"  Admiralty knot, exactly 6080 international feet/hour.  "kn"  Knot, exactly one Nautical mile per hour or exactly 1852/3600 m/s. Note that this is not an Admiralty knot (“admkn”).  "m/h" or "m/hr" *  Meters per hour  "m/s" or "m/sec" *  Meters per second  "mph"  Miles per hour (international miles) 


 
Temperature  "C" ("cel")  degrees Celsius  "F" ("fah")  degrees Fahrenheit  "K" ("kel") *  Kelvin  "Rank"  degrees Rankine  "Reau"  degrees Réaumur; °C = °Ré · 5/4. 


 
Time  "day" or "d"  Day (exactly 24 hours)  "hr"  Hour (exactly 60 minutes)  "mn" or "min"  Minute (exactly 60 seconds)  "sec" or "s" *  Second (“s” is the official abbreviation of this SI base unit, while “sec” is its traditional abbreviation in the CONVERT function) *  "yr"  Year (exactly 365.25 days, for purposes of this function) 


 
Volume  "ang3" or "ang^3" *  Cubic angstrom  "barrel"  U.S. oil barrel, exactly 42 U.S. customary gallons (liquid). Note that many other units are also called barrels (e.g., a beer barrel in the U.K. is 36 Imperial gallons)  "bushel"  U.S. bushel (not Imperial bushel), interpreted as volume  "cup"  Cup (U.S. customary liquid measure)  "ft3" or "ft^3"  Cubic international feet  "gal"  Gallon (U.S. customary liquid measure), 3.785411784 liters.  "GRT" ("regton")  Gross Registered Ton, 100 cubic (international) feet  "in3" or "in^3"  Cubic international inch  "l" or "L" ("lt") *  Liter  "ly3" or "ly^3"  Cubic lightyear  "m3" or "m^3" *  Cubic meter  "mi3" or "mi^3"  Cubic international mile  "MTON"  Measurement ton aka “freight ton”, 40 cubic feet  "Nmi3" or "Nmi^3"  Cubic nautical mile  "oz"  Fluid ounce (U.S. customary liquid measure; see “ozm” for ounce mass)  "Pica3" or "Pica^3" "picapt3" or "picapt^3"  Cubic Pica Point (one Pica point is 1/72 inch)  “pica3” or “pica^3”  Cubic Pica (one Pica is 1/6 inch)  "pt" or "us_pt"  U.S. Pint (liquid measure)  "qt"  Quart (U.S. customary liquid measure). This is 0.946352946 liters, and thus not the same as the U.S. dry quart (1.101220 liters), nor is this the same as the Imperial quart (as used in the U.K. and Canada, which is 1.1365225 liters exactly)  "tbs"  Tablespoon (U.S. customary, traditional meaning). This shall be 0.5 U.S. fluid ounce, not 15mL (common in U.S.) or 20mL (common in Australia).  "tsp"  Teaspoon (U.S. customary, traditional meaning), 1/6 fluid ounce in U.S. customary measure. This is not the 1/8 Imperial fl. oz. per Imperial units nor the modern teaspoon of 5 mL currently used in the U.S.; see “tspm”  "tspm"  Modern teaspoon, 5mL  "uk_gal"  U.K. / Imperial gallon, 4.54609 liters.  "uk_pt"  U.K. / Imperial pint,1/8 of a UK gallon.  "uk_qt"  U.K. / Imperial quart,1/4 of a UK gallon.  "yd3" or "yd^3"  Cubic international yard 


 
If a conversion factor (as listed above) is not exact, an implementation may use a more accurate conversion factor instead.
Implementationdefined unit names should contain a 'FULL STOP' (U+002E) character.
Evaluators shall support decimal prefixes for unit symbols marked with * and binary prefixes for unit symbols marked with †. Evaluators should not support prefixes for other unit symbols.
The unit symbols in parentheses are deprecated unit symbols; evaluators shall support these unit symbols.
Evaluators should use internationallystandardized unit name abbreviations for such additions where possible. Evaluators may support the obsolete symbols “p” and “P” as unit names for Pascals.
For purposes of this function, a year is exactly 365.25 days long.
Evaluators claiming to support this function shall permit the following unit decimal prefixes to be prepended to any unit symbol marked with “*” in the unit table cell above. Adding a unit prefix indicates multiplication of the (scalar) unit by the given prefix value; for example km indicates kilometres, and km2 or km^2 indicate square kilometres.
Table 25  Decimal Prefixes for use in CONVERT
Unit Prefix  Description  Prefix Value 
"Y"  yotta  1E+24 
"Z"  zetta  1E+21 
"E"  exa  1E+18 
"P"  peta  1E+15 
"T"  tera  1E+12 
"G"  giga  1E+09 
"M"  mega  1E+06 
"k"  kilo  1E+03 
"h"  hecto  1E+02 
“da” or "e"  deka ( Note: “e” is not a standard SI prefix  1E+01 
"d"  deci  1E01 
"c"  centi  1E02 
"m"  milli  1E03 
"u"  micro Note: this is “u”, not the standard SI µ  1E06 
"n"  nano  1E09 
"p"  pico  1E12 
"f"  femto  1E15 
"a"  atto  1E18 
"z"  zepto  1E21 
"y"  yocto  1E24 
The prefix “e” for 10 1 is nonstandard and included for backward compatibility with legacy applications and documents.
The unit names marked with † in the unit symbol table above (see the Information group) shall also support the following binary prefixes per IEC 600272:
Table 26  Binary prefixes for use in CONVERT
Binary Unit Prefix  Description  Prefix Value  Derived from 
"Yi"  yobi  2^80 = 1 208 925 819 614 629 174 706 176  yotta 
"Zi"  zebi  2^70 = 1 180 591 620 717 411 303 424  zetta 
"Ei"  exbi  2^60 = 1 152 921 504 606 846 976  exa 
"Pi"  pebi  2^50 = 1 125 899 906 842 624  peta 
"Ti"  tebi  2^40 = 1 099 511 627 776  tera 
"Gi"  gibi  2^30 = 1 073 741 824  giga 
"Mi"  mebi  2^20 = 1 048 576  mega 
"Ki"  kibi  2^10 = 1024  kilo 
In the case where there is a naming conflict (a unit name with a prefix is the same as an unprefixed name), the unprefixed name shall take precedence.
Evaluators may implement this conversion by first converting to some SI unit (e.g., meter and kilogram), and then convert again to the final unit.
See also EUROCONVERT 6.16.29
Summary: Return the cosine of an angle specified in radians.
Syntax: COS( Number N )
Returns: Number
Constraints: None
Semantics: Computes the cosine of an angle specified in radians.
See also ACOS 6.16.3, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the hyperbolic cosine of the given hyperbolic angle
Syntax: COSH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic cosine of a hyperbolic angle. The hyperbolic cosine is an analog of the ordinary (circular) cosine. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.
See also ACOSH 6.16.4, SINH 6.16.56, TANH 6.16.70
Summary: Return the cotangent of an angle specified in radians
Syntax: COT( Number N )
Returns: Number
Constraints: None
Semantics: Computes the cotangent of an angle specified in radians.
COT(x) = 1 / TAN(x)
See also ACOT 6.16.5, TAN 6.16.69, RADIANS 6.16.49, DEGREES 6.16.25, SIN 6.16.55, COS 6.16.19
Summary: Return the hyperbolic cotangent of the given hyperbolic angle
Syntax: COTH( Number N )
Returns: Number
Constraints: N<>0
Semantics: Computes the hyperbolic cotangent of a hyperbolic angle. The hyperbolic cotangent is an analog of the ordinary (circular) cotangent.
See also ACOSH 6.16.4, SINH 6.16.56, TANH 6.16.70
Summary: Return the cosecant of an angle specified in radians.
Syntax: CSC( Number N )
Returns: Number
Constraints: None
Semantics: Computes the cosecant cosine of an angle specified in radians. Equivalent to:
1/SIN(N)
See also SIN 6.16.55
Summary: Return the hyperbolic cosecant of the given angle specified in radians
Syntax: CSCH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic cosecant of a hyperbolic angle. This is equivalent to:
1/SINH(N)
See also SINH 6.16.56, CSCH
Summary: Convert radians to degrees.
Syntax: DEGREES( Number N )
Returns: Number
Constraints: None
Semantics: Converts a number in radians into a number in degrees. DEGREES(N) is equal to N*180/PI().
See also RADIANS 6.16.49, PI 6.16.45
Summary: Report if two numbers are equal, returns 1 if they are equal.
Syntax: DELTA( Number X [ ; Number Y = 0 ] )
Returns: Number
Constraints: None
Semantics: If X and Y are equal, return 1, else 0. Y is set to 0 if omitted.
See also Infix operator “=” 6.4.7
Summary: Calculates the error function.
Syntax: ERF( Number z0 [ ; Number z1 ] )
Returns: Number
Constraints: None
Semantics: With a single argument, returns the error function of z0:
With two arguments, returns
See also ERFC 6.16.28
Summary: Calculates the complementary error function.
Syntax: ERFC( Number z )
Returns: Number
Constraints: None
Semantics: returns the complementary error function of z: ERFC(z) = 1 – ERF(z)
See also ERF 6.16.27
Summary: Converts a Number, representing a value in one European currency, to an equivalent value in another European currency, according to the fixed conversion rates defined by the Council of the European Union.
Syntax: EUROCONVERT( Number N ; Text From ; Text To [ ; Logical FullPrecision = FALSE() [ ; Integer TriangulationPrecision ] ] )
Returns: Currency
Constraints: From and To shall be known to the evaluator. TriangulationPrecision shall be >= 3, if not omitted.
If an evaluator does not support the parameters FullPrecision and TriangulationPrecision, FullPrecision should be assumed to be false.
Semantics: Returns the given money value of a conversion from From currency into To currency. Both From and To shall be the official [ISO4217] abbreviation for the given currency; note that these are in upper case, but the function accepts lower case or mixed case as well. If From and To are equal currencies, the value N is returned, no precision or triangulation is applied.
The function shall use the rates of exchange as set by the European Commission, as follows:
Table 27  EUROCONVERT
From  To  Rate  Currency  Decimals 
"EUR"  "ATS"  13.7603  Austrian Schilling  2 
"EUR"  "BEF"  40.3399  Belgian Franc  0 
"EUR"  "DEM"  1.95583  German Mark  2 
"EUR"  "ESP"  166.386  Spanish Peseta  0 
"EUR"  "FIM"  5.94573  Finnish Markka  2 
"EUR"  "FRF"  6.55957  French Franc  2 
"EUR"  "IEP"  0.787564  Irish Pound  2 
"EUR"  "ITL"  1936.27  Italian Lira  0 
"EUR"  "LUF"  40.3399  Luxembourg Franc  0 
"EUR"  "NLG"  2.20371  Dutch Guilder  2 
"EUR"  "PTE"  200.482  Portuguese Escudo  2 
"EUR"  "GRD"  340.750  Greek Drachma  2 
"EUR"  "SIT"  239.640  Slovenian Tolar  2 
“EUR”  “MTL”  0.429300  Maltese Lira  2 
“EUR”  “CYP”  0.585274  Cypriot Pound  2 
"EUR"  "SKK"  30.1260  Slovak Koruna  2 
As new member countries adopt the Euro, new conversion rates will become active and evaluators may add them using the respective [ISO4217] codes and fixed rates as defined by the European Council, on the basis of a European Commission proposal.
Note:
The European Commission's Euro entry page is http://ec.europa.eu/euro/
The conversion rates and triangulation rules are available at http://ec.europa.eu/economy_finance/euro/adoption/conversion/index_en.htm with links to the European Council Regulation legal documents at the http://eurlex.europa.eu/ European Union law database server.
If FullPrecision is omitted or False, the result is rounded according to the decimals of the To currency. If FullPrecision is True the result is not rounded.
If TriangulationPrecision is given and >=3, the intermediate result of a triangular conversion (currency1,EUR,currency2) is rounded to that precision. If TriangulationPrecision is omitted, the intermediate result is not rounded. Also if To currency is “EUR”, TriangulationPrecision precision is used as if triangulation was needed and conversion from EUR to EUR was applied.
See also CONVERT
Summary: Rounds a number up to the nearest even integer. Rounding is away from zero.
Syntax: EVEN( Number N )
Returns: Number
Constraints: None
Semantics: Returns the even integer whose sign is the same as N's and whose absolute value is greater than or equal to the absolute value of N.
See also ODD 6.16.44
Summary: Returns e raised by the given number.
Syntax: EXP( Number X )
Returns: Number
Constraints: None
Semantics: Computes
See also LOG 6.16.40, LN 6.16.39
Summary: Return factorial (!).
Syntax: FACT( Integer F )
Returns: Number
Constraints: F >= 0
Semantics: Return the factorial
F(0)=F(1)=1.
See also Infix Operator "*" 6.4.4, GAMMA 6.16.34
Summary: Returns double factorial (!!).
Syntax: FACTDOUBLE( Integer F )
Returns: Number
Constraints: F >= 0
Semantics: Return
Double factorial is computed by multiplying every other number in the 1..N range, with N always being included.
See also Infix Operator "*" 6.4.4, GAMMA 6.16.34, FACT 6.16.32
Summary: Return gamma function value.
Syntax: GAMMA( Number N )
Returns: Number
Constraints: N<>0 and N not a negative integer.
Semantics: Return
with Γ(N+1) = N * Γ(N). Note that for nonnegative integers N, Γ(N+1) = N! = FACT(N). Note that GAMMA can accept nonintegers.
See also FACT 6.16.32
Summary: Returns the natural logarithm of the GAMMA function.
Syntax: GAMMALN( Number X )
Returns: Number
Constraints: For each X, X > 0
Semantics: Returns the same value as =LN(GAMMA(X))
See also GAMMA 6.16.34, FACT 6.16.32
Summary: Returns the greatest common divisor (GCD)
Syntax: GCD( { NumberSequenceList X }+ )
Returns: Number
Constraints: For all a in X: INT(a) >= 0 and for at least one a in X: INT(a)>0
Semantics: Return the largest integer N such that for every a in X: INT(a) is a multiple of N.
Note: If for all a in X: INT(a)=0 the return value is implementationdefined but is either an Error or 0.
See also LCM 6.16.38
Summary: Returns 1 if a number is greater than or equal to another number, else returns 0.
Syntax: GESTEP( Number X [ ; Number Step = 0 ] )
Returns: Number
Semantics: Number X is tested against number Step. If greater or equal 1 is returned, else 0. The second parameter is assumed 0 if omitted. If one of the parameters is not a Number, the function results in an Error.
See also
Summary: Returns the least common multiplier
Syntax: LCM( { NumberSequenceList X }+ )
Returns: Number
Constraints: For all in X: INT(X)=X, X >= 0
Semantics: Return the smallest integer that is the multiple of the given values. Each value has INT applied to it first. Note that if given two numbers, ABS(a*b)=LCM(a;b)*GCD(a;b).
See also GCD 6.16.36
Summary: Return the natural logarithm of a number.
Syntax: LN( Number X )
Returns: Number
Constraints: X>0
Semantics: Computes the natural logarithm (base e) of the given number.
See also LOG 6.16.40, LOG10 6.16.41, POWER 6.16.46, EXP 6.16.31
Summary: Return the logarithm of a number in a specified base.
Syntax: LOG( Number N [ ; Number Base = 10 ] )
Returns: Number
Constraints: N > 0
Semantics: Computes the logarithm of a number in the specified base. Note that if the base is not specified, the logarithm base 10 is returned.
See also LOG10 6.16.41, LN 6.16.39, POWER 6.16.46, EXP 6.16.31
Summary: Return the base 10 logarithm of a number.
Syntax: LOG10( Number N )
Returns: Number
Constraints: N > 0
Semantics: Computes the base 10 logarithm of a number.
See also LOG 6.16.40, LN 6.16.39, POWER 6.16.46, EXP 6.16.31
Summary: Return the remainder when one number is divided by another number.
Syntax: MOD( Number a ; Number b )
Returns: Number
Constraints: b != 0
Semantics: Computes the remainder of a/b. The remainder has the same sign as b.
See also Infix Operator "/" 6.4.5, QUOTIENT 6.16.48
Summary: Returns the multinomial for the given values.
Syntax: MULTINOMIAL( { NumberSequence A }+ )
Returns: Number
Constraints: None
Semantics: Returns the multinomial of the sequence A = (a1, a2, ..., an). Multinomial is defined as FACT(a1+a2+...+an) / (FACT(a1)*FACT(a2)*...*FACT(an))
See also FACT 6.16.32
Summary: Rounds a number up to the nearest odd integer, where "up" means "away from 0".
Syntax: ODD( Number N )
Returns: Number
Constraints: None
Semantics: Returns the odd integer whose sign is the same as N's and whose absolute value is greater than or equal to the absolute value of N. In other words, any "rounding" is away from zero. By definition, ODD(0) is 1.
See also EVEN 6.16.30
Summary: Return the approximate value of Pi.
Syntax: PI()
Returns: Number
Constraints: None.
Semantics: This function takes no arguments and returns the (approximate) value of pi. Evaluators should use the closest possible numerical representation that is possible in their representation of numbers.
See also SIN 6.16.55, COS 6.16.19
Summary: Return the value of one number raised to the power of another number.
Syntax: POWER( Number a ; Number b )
Returns: Number
Constraints: None
Semantics: Computes a raised to the power b.
•.POWER(0,0) is implementationdefined, but shall be one of 0,1, or an Error.
•.POWER(0,b), where b < 0, shall return an Error.
•.POWER(a,b), where a<=0 and INT(b)!=b, is implementationdefined.
See also LOG 6.16.40, LOG10 6.16.41, LN 6.16.39, EXP 6.16.31
Summary: Multiply the set of numbers, including all numbers inside ranges
Syntax: PRODUCT( { NumberSequence N }+ )
Returns: Number
Constraints: None
Semantics: Returns the product of the Numbers (and only the Numbers, i.e., not Text inside ranges). This is equivalent to SUM except that it uses the * operator instead of +.
See also SUM 6.16.61
Summary: Return the integer portion of a division.
Syntax: QUOTIENT( Number A ; Number B )
Returns: Number
Constraints: B <> 0
Semantics: Return the integer portion of a division.
See also MOD 6.16.42
Summary: Convert degrees to radians.
Syntax: RADIANS( Number N )
Returns: Number
Constraints: None
Semantics: Converts a number in degrees into a number in radians. RADIANS(N) is equal to N*PI()/180.
See also DEGREES 6.16.25, PI 6.16.45
Summary: Return a random number between 0 (inclusive) and 1 (exclusive).
Syntax: RAND()
Returns: Number
Semantics: This function takes no arguments and returns a random number between 0 (inclusive) and 1 (exclusive). Note that unlike most functions, this function will typically return different values when called each time with the same (empty set of) parameters.
See also RANDBETWEEN 6.16.51
Summary: Return a random integer number between A and B.
Syntax: RANDBETWEEN( Integer A ; Integer B )
Returns: Integer
Constraints: A <= B
Semantics: The function returns a random integer number between A and B inclusive. Note that unlike most functions, this function will often return different values when called each time with the same parameters.
See also RAND 6.16.50
Summary: Return the secant of an angle specified in radians.
Syntax: SEC( Number N )
Returns: Number
Constraints: None
Semantics: Computes the secant cosine of an angle specified in radians. Equivalent to:
1/COS(N)
See also SIN 6.16.55
Summary: Returns the sum of a power series.
Syntax: SERIESSUM( Number X ; Number N ; Number M ; Array Coefficients )
Returns: Number
Constraints:
All elements of Coefficients are of type Number.
X < > 0 if any of the exponents, which are generated from N and M, are negative.
Semantics: Returns a sum of powers of the number X.
With C being the number of coefficients the function is computed as:
Summary: Return the sign of a number
Syntax: SIGN( Number N )
Returns: Number
Constraints: None
Semantics: If N < 0, returns 1; if N > 0, returns +1; if N == 0, returns 0.
See also ABS 6.16.2
Summary: Return the sine of an angle specified in radians
Syntax: SIN( Number N )
Returns: Number
Constraints: None
Semantics: Computes the sine of an angle specified in radians.
See also ASIN 6.16.7, RADIANS 6.16.49, DEGREES 6.16.25
Summary: Return the hyperbolic sine of the given hyperbolic angle
Syntax: SINH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic sine of a hyperbolic angle. The hyperbolic sine is an analog of the ordinary (circular) sine. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.
See also ASINH 6.16.8, COSH 6.16.20, TANH 6.16.70
Summary: Return the hyperbolic secant of the given angle specified in radians
Syntax: SECH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic secant of a hyperbolic angle. This is equivalent to:
1/COSH(N)
See also SINH 6.16.56, CSCH
Summary: Return the square root of a number
Syntax: SQRT( Number N )
Returns: Number
Constraints: N>=0
Semantics: Returns the square root of a nonnegative number. This function shall produce an Error if given a negative number; for producing complex numbers, see IMSQRT.
See also POWER 6.16.46, IMSQRT 6.8.24, SQRTPI 6.16.59
Summary: Return the square root of a number multiplied by pi.
Syntax: SQRTPI( Number N )
Returns: Number
Constraints: N>=0
Semantics: Returns the square root of a nonnegative number after it was first multiplied by PI, that is, SQRT(N*PI()). This function shall produce an Error if given a negative number; for producing complex numbers, see IMSQRT.
See also POWER 6.16.46, SQRT 6.16.58, PI 6.16.45, IMSQRT 6.8.24
Summary: Evaluates a function on a range.
Syntax: SUBTOTAL( Integer function ; NumberSequence sequence )
Returns: Number
Constraints: None
Semantics: Computes a given function on a number sequence. Function is denoted by the first parameter: The difference from standard functions is that all members of the sequence are excluded which:
Function  Exclude hidden by filter  Exclude hidden by filter or collapsed 
AVERAGE  1  101 
COUNT  2  102 
COUNTA  3  103 
MAX  4  104 
MIN  5  105 
PRODUCT  6  106 
STDEV  7  107 
STDEVP  8  108 
SUM  9  109 
VAR  10  110 
VARP  11  111 
See also SUM 6.16.61, AVERAGE 6.18.3
Summary: Sum (add) the set of numbers, including all numbers in ranges
Syntax: SUM( { NumberSequenceList N }+ )
Returns: Number
Constraints: N != {}; Evaluators may evaluate expressions that do not meet this constraint.
Semantics: Adds Numbers (and only Numbers) together (see the text on conversions).
See also AVERAGE 6.18.3
Summary: Sum the values of cells in a range that meet a criteria.
Syntax: SUMIF( ReferenceListReference R ; Criterion C [ ; Reference S ] )
Returns: Number
Constraints: Does not accept constant values as the range parameter.
Semantics: Sums the values of type Number in the range R or S that meet the Criterion C (4.11.8).
If S is not given, R may be a reference list. If S is given, R shall not be a reference list with more than 1 references and an Error be generated if it was.
If the optional range S is included, then the values of S starting from the top left cell and matching the geometry of R (same number of rows and columns) are summed if the corresponding value in R meets the Criterion. The actual range S is not considered. If the resulting range exceeds the sheet bounds, column numbers larger than the maximum column and row numbers larger than the maximum row are silently ignored, no Error is generated for this case.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also COUNTIF 6.13.9, SUM 6.16.61, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: Sum the values of cells in a range that meet multiple criteria in multiple ranges.
Syntax: SUMIFS( Reference R ; Reference R1 ; Criterion C1 [ ; Reference R2 ; Criterion C2 ]... )
Returns: Number
Constraints: Does not accept constant values as the reference parameter.
Semantics: Sums the value of cells in range R that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.8). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; an entry is counted only if the same position in each array is the result of a criteria match.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also AVERAGEIFS 6.18.6, COUNTIFS 6.13.10, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: Returns the sum of the products of the matrix elements.
Syntax: SUMPRODUCT( { ForceArray Array A }+ )
Returns: Number
Constraints: All matrices shall have the same dimensions.
Semantics: Multiplies the corresponding elements of all matrices and returns the sum of them.
Summary: Sum (add) the set of squares of numbers, including all numbers in ranges
Syntax: SUMSQ( { NumberSequence N }+ )
Returns: Number
Constraints: N != {}; Evaluators may evaluate expressions that do not meet this constraint.
Semantics: Adds squares of Numbers (and only Numbers) together. See the text on conversions.
Summary: Returns the sum of the difference between the squares of the matrices A and B.
Syntax: SUMX2MY2( ForceArray Array A ; ForceArray Array B )
Returns: Number
Constraints: Both matrices shall have the same dimensions.
Semantics: Sums up the differences of the corresponding elements squares for two matrices.
Summary: Returns the total sum of the squares of the matrices A and B.
Syntax: SUMX2PY2( ForceArray Array A ; ForceArray Array B )
Returns: Number
Constraints: Both matrices shall have the same dimensions.
Semantics: Sums up the squares of each element of the two matrices.
Summary: Returns the sum of the squares of the differences between matrix A and B.
Syntax: SUMXMY2( ForceArray Array A ; ForceArray Array B )
Returns: Number
Constraints: Both matrices shall have the same dimensions.
Semantics: Sums up the squares of the differences of the corresponding elements for two matrices.
Summary: Return the tangent of an angle specified in radians
Syntax: TAN( Number N )
Returns: Number
Constraints: None
Semantics: Computes the tangent of an angle specified in radians.
TAN(x) = SIN(x) / COS(x)
See also ATAN 6.16.9, ATAN2 6.16.10, RADIANS 6.16.49, DEGREES 6.16.25, SIN 6.16.55, COS 6.16.19, COT 6.16.21
Summary: Return the hyperbolic tangent of the given hyperbolic angle
Syntax: TANH( Number N )
Returns: Number
Constraints: None
Semantics: Computes the hyperbolic tangent of a hyperbolic angle. The hyperbolic tangent is an analog of the ordinary (circular) tangent. The points (cosh t, sinh t) define the right half of the equilateral hyperbola, just as the points (cos t, sin t) define the points of a circle.
See also ATANH 6.16.11, SINH 6.16.56, COSH 6.16.20, FISHERINV 6.18.27
Summary: Round a number N up to the nearest multiple of the second parameter, significance.
Syntax: CEILING( Number N [ ; [ Number significance ] [ ; Number mode ] ] )
Returns: Number
Constraints: Both N and significance shall be numeric and have the same sign if not 0.
Semantics: Rounds a number up to a multiple of the second number. If significance is omitted or an empty parameter (two consecutive ;; semicolons) it is assumed to be 1 if N is negative and +1 if N is nonnegative, making the function act like the normal mathematical ceiling function if mode is not given or zero. If mode is given and not equal to zero, the absolute value of N is rounded away from zero to a multiple of the absolute value of significance and then the sign applied . If mode is omitted or zero, rounding is toward positive infinity; the number is rounded to the smallest multiple of significance that is equalto or greater than N. If any of the two parameters N or significance is zero, the result is zero.
Note: Many application user interfaces have a CEILING function with only two parameters, and somewhat different semantics than given here (e.g., they operate as if there was a nonzero mode value). These CEILING functions are inconsistent with the standard mathematical definition of CEILING.
See also FLOOR 6.17.3, INT 6.17.2
Summary: Rounds a number down to the nearest integer.
Syntax: INT( Number N )
Returns: Number
Constraints: None
Semantics: Returns the nearest integer whose value is less than or equal to N. Rounding is towards negative infinity.
See also ROUND 6.17.5, TRUNC 6.17.8
Summary: Round a number N down to the nearest multiple of the second parameter, significance.
Syntax: FLOOR( Number N [ ; [ Number significance ] [ ; Number mode ] ] )
Returns: Number
Constraints: Both N and significance shall be numeric and have the same sign.
Semantics: Rounds a number down to a multiple of the second number. If significance is omitted or an empty parameter (two consecutive ;; semicolons) it is assumed to be 1 if N is negative and +1 if N is nonnegative, making the function act like the normal mathematical floor function if mode is not given or zero. If mode is given and not equal to zero, the absolute value of N is rounded away from zero to a multiple of the absolute value of significance and then the sign applied . Otherwise, it rounds toward negative infinity, and the result is the largest multiple of significance that is less than or equal to N. If any of the two parameters N or significance is zero, the result is zero.
Note: Many application user interfaces have a FLOOR function with only two parameters, and somewhat different semantics than given here (e.g., they operate as if there was a nonzero mode value). These FLOOR functions are inconsistent with the standard mathematical definition of FLOOR.
See also CEILING 6.17.1, INT 6.17.2
Summary: Rounds the number to given multiple.
Syntax: MROUND( Number a ; Number b )
Returns: Number
Constraints: None
Semantics: Returns the number X, for which the following holds: X/b=INT(X/b) (b divides X), and for any other Y with the same property, ABS(Ya)>=ABS(Xa). In case that two such X exist, the greater one is the result. In less formal language, this function rounds the number a to multiples of b.
See also ROUND 6.17.5
Summary: Rounds the value X to the nearest multiple of the power of 10 specified by Digits.
Syntax: ROUND( Number X [ ; Number Digits = 0 ] )
Returns: Number
Constraints: None
Semantics: Round number X to the precision specified by Digits. The number X is rounded to the nearest power of 10 given by 10 −Digits. If Digits is zero, or absent, round to the nearest decimal integer. If Digits is nonnegative, round to the specified number of decimal places. If Digits is negative, round to the left of the decimal point by Digits places. If X is halfway between the two nearest values, the result shall round away from zero. Note that if X is a Number, and Digits <= 0, the results will always be an integer (without a fractional component).
See also TRUNC 6.17.8, INT 6.17.2
Summary: Rounds the value X towards zero to the number of digits specified by Digits
Syntax: ROUNDDOWN( Number X [ ; Integer Digits = 0 ] )
Returns: Number
Constraints: None
Semantics: Round X towards zero, to the precision specified by Digits. The number returned is a multiple of 10−Digits. If Digits is zero, or absent, round to the largest decimal integer whose absolute value is smaller or equal to the absolute value of X.
If Digits is positive, round towards zero to the specified number of decimal places. If Digits is negative, round towards zero to the left of the decimal point by Digits places.
See also TRUNC 6.17.8, INT 6.17.2, ROUND 6.17.5, ROUNDUP 6.17.7
Summary: Rounds the value X away from zero to the number of digits specified by Digits
Syntax: ROUNDUP( Number X [ ; Integer Digits = 0 ] )
Returns: Number
Constraints: None
Semantics: Round X away from zero, to the precision specified by Digits. The number returned is a multiple of 10−Digits. If Digits is zero, or absent, round to the smallest decimal integer whose absolute value is larger or equal to the absolute value of X. If Digits is positive, round away from zero to the specified number of decimal places. If Digits is negative, round away from zero to the left of the decimal point by Digits places.
See also TRUNC 6.17.8, INT 6.17.2, ROUND 6.17.5, ROUNDDOWN 6.17.6
Summary: Truncate a number to a specified number of digits.
Syntax: TRUNC( Number a ; Integer b )
Returns: Number
Constraints: None
Semantics: Truncate number a to the number of digits specified by b. If b is zero, or absent, truncate to a decimal integer. If b is positive, truncate to the specified number of decimal places. If b is negative, truncate to the left of the decimal point.
See also ROUND 6.17.5, INT 6.17.2
The following are statistical functions (functions that report information on a set of numbers). Some functions that could also be considered statistical functions, such as SUM, are listed elsewhere.
Summary: Calculates the average of the absolute deviations of the values in list.
Syntax: AVEDEV( { NumberSequenceList N }+ )
Returns: Number
Constraints: None.
Semantics:
See also SUM, AVERAGE
Summary: Average the set of numbers
Syntax: AVERAGE( { NumberSequence N }+ )
Returns: Number
Constraints: At least one Number included. Returns an Error if no Numbers provided.
Semantics: Computes SUM(List) / COUNT(List).
See also SUM 6.16.61, COUNT 6.13.6
Summary: Average values, including values of type Text and Logical.
Syntax: AVERAGEA( { Any N }+ )
Returns: Number
Constraints: At least one value included. Returns an Error if no value provided.
Semantics: A variant of the AVERAGE function that includes values of type Text and Logical. Text values are treated as number 0. Logical True is treated as 1 and False is treated as 0. Empty cells are not included. Any N may be of type ReferenceList.
See also AVERAGE 6.18.3
Summary: Average the values of cells in a range that meet a criteria.
Syntax: AVERAGEIF( Reference R ; Criterion C [ ; Reference A ] )
Returns: Number
Constraints: Does not accept constant values as reference parameters.
Semantics: If reference A is omitted, averages the values of cells in the reference range R that meet the Criterion C (4.11.8). If reference A is given, averages the values of cells of a range that is constructed using the top left cell of reference A and applying the dimensions, shape and size, of reference R. If no cell in range R matches the Criterion C, an Error is returned. If no Numbers are in the range to be averaged, an Error is returned.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also AVERAGEIFS 6.18.6, COUNTIF 6.13.9, SUMIF 6.16.62, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: Average the values of cells that meet multiple criteria in multiple ranges.
Syntax: AVERAGEIFS( Reference A ; Reference R1 ; Criterion C1 [ ; Reference R2 ; Criterion C2 ]... )
Returns: Number
Constraints: Does not accept constant values as reference parameters.
Semantics: Averages the values of cells in the reference range A that meet the Criterion C1 in the reference range R1 and the Criterion C2 in the reference range R2, and so on (4.11.8). All reference ranges shall have the same dimension and size, else an Error is returned. A logical AND is applied between each array result of each selection; a cell of reference range A is evaluated only if the same position in each array is the result of a Criterion match. If no numbers are in the result set to be averaged, an Error is returned.
The values returned may vary depending upon the HOSTUSEREGULAREXPRESSIONS or HOSTUSEWILDCARDS or HOSTSEARCHCRITERIAMUSTAPPLYTOWHOLECELL properties. 3.4
See also AVERAGEIF 6.18.5, COUNTIFS 6.13.10, SUMIFS 6.16.63, Infix Operator "=" 6.4.7, Infix Operator "<>" 6.4.8, Infix Operator Ordered Comparison ("<", "<=", ">", ">=") 6.4.9
Summary: returns the value of the probability density function or the cumulative distribution function for the beta distribution.
Syntax: BETADIST( Number x ; Number a ; Number b [ ; Number a = 0 [ ; Number b = 1 [ ; Logical Cumulative = TRUE() ] ] ] )
Returns: Number
Constraints: a > 0, b > 0, a < b,
If a < 1, then the density function has a pole at x = a.
If b < 1, then the density function has a pole at x = b.
In both cases, if x=a respectively x=b and Cumulative=FALSE(), an Error is returned.
Semantics: If Cumulative is FALSE(), BETADIST returns 0 if x < a or x > b and the value
otherwise.
If Cumulative is TRUE(), BETADIST returns 0 if x < a, 1 if x > b, and the value
otherwise.
Note: With substitution
the term can be written as
See also BETAINV 6.18.8
Summary: returns the inverse of BETADIST(x;a;b;a;b;TRUE()).
Syntax: BETAINV( Number p ; Number a ; Number b [ ; Number a = 0 [ ; Number b = 1 ] ] )
Returns: Number
Semantics: BETAINV returns the unique number x in the closed interval from a to b such that BETADIST(x;a;b;a;b) = p.
See also BETADIST 6.18.7
Summary: Returns the probability of a trial result using binomial distribution.
Syntax: BINOM.DIST.RANGE( Integer N ; Number P ; Integer S [ ; Integer S2 ] )
Returns: Number
Constraints: 0<=P<=1, 0<=S<=S2<=N
Semantics: Let N be a total number of independent trials, and P be a probability of success for each trial. This function returns the probability that the number of successful trials shall be exactly S. If the optional parameter S2 is provided, this function returns the probability that the number of successful trials shall lie between S and S2 inclusive.
This function is computed as follows:
If S2 is not given, let S2:=S. Then the function returns the value of
See also BINOMDIST 6.18.10
Summary: Returns the binomial distribution.
Syntax: BINOMDIST( Integer S ; Integer N ; Number P ; Logical Cumulative )
Returns: Number
Constraints: 0 <= P <= 1; 0 <= S <= N
Semantics: If Cumulative is FALSE(), this function returns the same result as BINOM.DIST.RANGE(N;P;S). If Cumulative is TRUE(), it is equivalent to calling BINOM.DIST.RANGE(N;P;0;S).
See also BINOM.DIST.RANGE 6.18.9
Summary: returns the righttail probability for the c2distribution.
Syntax: LEGACY.CHIDIST( Number x ; Number DegreesOfFreedom )
Returns: Number
Constraints: DegreesOfFreedom is a positive integer.
See also CHISQDIST 6.18.12, LEGACY.CHITEST 6.18.15
Summary: returns the value of the probability density function or the cumulative distribution function for the c2distribution.
Syntax: CHISQDIST( Number x ; Number DegreesOfFreedom [ ; Logical Cumulative = TRUE() ] )
Returns: Number
Constraints: DegreesOfFreedom is a positive integer.
Semantics: In the following n is DegreesOfFreedom.
See also LEGACY.CHIDIST 6.18.11
Summary: returns the inverse of LEGACY.CHIDIST(x; DegreesOfFreedom).
Syntax: LEGACY.CHIINV( Number p ; Number DegreesOfFreedom )
Returns: Number
Semantics: LEGACY.CHIINV returns the unique number x such that LEGACY.CHIDIST(x; DegreesOfFreedom) = p.
See also LEGACY.CHIDIST 6.18.11
Summary: returns the inverse of CHISQDIST(x; DegreesOfFreedom; TRUE()).
Syntax: CHISQINV( Number p ; Number DegreesOfFreedom )
Returns: Number
See also CHISQDIST 6.18.12
Summary: Returns some Chi square goodnessforfit test.
Syntax: LEGACY.CHITEST( ForceArray Array A ; ForceArray Array E )
Returns: Number
Constraints:
ROWS(A) == ROWS(E)
COLUMNS(A) == COLUMNS(E)
COLUMNS(A) * ROWS(A) > 1
Semantics:
For an empty element or an element of type Text or Boolean in A the element at the corresponding position of E is ignored, and vice versa.
First a Chi square statistic is calculated:
Then LEGACY.CHIDIST is called with the Chisquare value and a degree of freedom (df):
See also LEGACY.CHIDIST 6.18.11
Summary: Returns the confidence interval for a population mean.
Syntax: CONFIDENCE( Number alpha ; Number stddev ; Number size )
Returns: Number
Constraints: 0 < alpha < 1; stddev > 0, size >= 1
Semantics: Calling this function is equivalent to calling NORMINV(1  alpha / 2; 0; 1) * stddev / SQRT (size)
Summary: Calculates the correlation coefficient of values in N1 and N2.
Syntax: CORREL( ForceArray Array N1 ; ForceArray Array N2 )
Returns: Number
Constraints: COLUMNS(N1) = COLUMNS(N2), ROWS(N1) = ROWS(N2), both sequences shall contain at least one number at corresponding positions each.
Semantics: Has the same value as COVAR(N1;N2)/STDEVP(N1)*(STDEVP(N2)). The CORREL function actually is identical to the PEARSON function.
For an empty element or an element of type Text or Boolean in N1 the element at the corresponding position of N2 is ignored, and vice versa.
See also PEARSON 6.18.56
Summary: Calculates covariance of two cell ranges.
Syntax: COVAR( ForceArray Array n1 ; ForceArray Array n2 )
Returns: Number
Constraints: COLUMNS(n1) = COLUMNS(n2), ROWS(n1) = ROWS(n2), both sequences shall contain at least one number at corresponding positions each.
Semantics: returns
For an empty element or an element of type Text or Boolean in n1 the element at the corresponding position of n2 is ignored, and vice versa.
Summary: Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value.
Syntax: CRITBINOM( Number Trials ; Number SP ; Number Alpha )
Returns: Number
Constraints: Trials >=0, 0 <= SP <= 1, Alpha >= 1
Semantics:
Trials is the total number of trials.
SP is the probability of success for one trial.
Alpha is the threshold probability to be reached or exceeded.
Summary: Calculates sum of squares of deviations.
Syntax: DEVSQ( { NumberSequence n }+ )
Returns: Number
Semantics: returns
where a is the result of calling AVERAGE(n).
Summary: returns the value of the probability density function or the cumulative distribution function for the exponential distribution.
Syntax: EXPONDIST( Number x ; Number l [ ; Logical Cumulative = TRUE() ] )
Returns: Number
Constraints: l > 0
Semantics: If Cumulative is FALSE(), EXPONDIST returns 0 if x < 0 and the value
otherwise.
If Cumulative is TRUE(), EXPONDIST returns 0 if x < 0 and the value
otherwise.
Summary: returns the value of the probability density function or the cumulative distribution function for the Fdistribution.
Syntax: FDIST( Number x ; Number r1 ; Number r2 [ ; Logical Cumulative = TRUE() ] )
Returns: Number
Constraints: r1 and r2 are positive integers
Semantics:
r1 is the degrees of freedom in the numerator of the F distribution.
r2 is the degrees of freedom in the denominator of the F distribution.
If Cumulative is FALSE(), FDIST returns 0 if x < 0, an Error if the numerator degrees of freedom r1 = 1 and x = 0, and the value
otherwise.
If Cumulative is TRUE(), FDIST returns 0 if x < 0 and the value
otherwise.
See also LEGACY.FDIST 6.18.23
Summary: returns the area of the right tail of the probability density function for the Fdistribution.
Syntax: LEGACY.FDIST( Number x ; Number r1 ; Number r2 )
Returns: Number
Constraints: r1 and r2 are positive integers
Semantics:
LEGACY.FDIST returns Error if x < 0 and the value
otherwise.
Note that the latter is (1FDIST(x; r1; r2;TRUE())).
See also FDIST 6.18.22
Summary: returns the inverse of FDIST(x;r1;r2;TRUE()).
Syntax: FINV( Number p ; Number r1 ; Number r2 )
Returns: Number
Semantics: FINV returns the unique nonnegative number x such that FDIST(x;r1;r2) = p.
See also FDIST 6.18.22, LEGACY.FDIST 6.18.23, LEGACY.FINV 6.18.25
Summary: returns the inverse of LEGACY.FDIST(x;r1;r2).
Syntax: LEGACY.FINV( Number p ; Number r1 ; Number r2 )
Returns: Number
Semantics: LEGACY.FINV returns the unique nonnegative number x such that LEGACY.FDIST(x;r1;r2) = p.
See also FDIST 6.18.22, LEGACY.FDIST 6.18.23, FINV 6.18.24
Summary: returns the Fisher transformation.
Syntax: FISHER( Number r )
Returns: Number
Constraints: 1 < r < 1
Semantics: Returns the Fisher transformation with a sample correlation r. This function computes
where ln is the natural logarithm function.
FISHER is a synonym for ATANH.
See also ATANH 6.16.11
Summary: returns the inverse Fisher transformation.
Syntax: FISHERINV( Number r )
Returns: Number
Constraints: none
Semantics: Returns the inverse Fisher transformation. This function computes
FISHERINV is a synonym for TANH.
See also TANH 6.16.70
Summary: Extrapolates future values based on existing x and y values.
Syntax: FORECAST( Number Value ; ForceArray Array Data_Y ; ForceArray Array Data_X )
Returns: Number
Constraints: COLUMNS(Data_Y) = COLUMNS(Data_X), ROWS(Data_Y) = ROWS(Data_X)
Semantics:
Value is the xvalue, for which the yvalue on the linear regression is to be returned.
Data_Y is the array or range of known yvalues.
Data_X is the array or range of known xvalues.
For an empty element or an element of type Text or Boolean in Data_Y the element at the corresponding position of Data_X is ignored, and vice versa.
Summary: Categorizes values into intervals and counts the number of values in each interval.
Syntax: FREQUENCY( NumberSequenceList data ; NumberSequenceList bins )
Returns: Array
Constraints: Values in bins shall be sorted in ascending order and bins shall be a column vector. Evaluators may accept unsorted values in bins.
Semantics: Counts the number of values for each interval given by the border values in bins .
The values in bins determine the upper boundaries of the intervals. The intervals include the upper boundaries. The returned array is a column vector and has one more element than bins ; the last element represents the number of all elements greater than the last value in bins . If bins is empty, all values in data are counted. The values in the result array are ordered matching the original order of bins . If the values in bins are not sorted in ascending order, they are sorted internally to form category intervals and the counts of data values are "unsorted" to the original order of bins. If data is empty, the value of all elements in the returned array is 0.
data The data, that should be categorized and counted according to the given intervals.
bins The upper boundaries determining the intervals the values in data should be grouped by.
Summary: Calculates the probability of an Ftest.
Syntax: FTEST( ForceArray NumberSequence Data_1 ; ForceArray NumberSequence Data_2 )
Returns: Number
Constraints: Data_1 and Data_2 shall both contain at least 2 numbers and shall both have nonzero variances
Semantics: Calculates the twotailed probability that, based on two samples from two normal distributions, these normal distributions have different variances.
Suppose the first sample has size n1 and sample variance s1^2 and the second sample has size n2 and sample variance s2^2. If s1^2>s^2 FDIST returns twice the area of the right tail of the Fdistribution with degrees of freedom n11,n21 beyond s^1/s^2. If s1^2<s^2 FDIST returns twice the area of the left tail of the Fdistribution with degrees of freedom n11,n21 below s^1/s^2.
See also TTEST 6.18.81
Summary: returns the value of the probability density function or the cumulative distribution function for the Gamma distribution.
Syntax: GAMMADIST( Number x ; Number a ; Number [ ; Logical Cumulative = TRUE() ] )
Returns: Number
Constraints: a > 0, > 0
Semantics: If Cumulative is FALSE(), GAMMADIST returns 0 if x < 0 and the value
otherwise.
If Cumulative is TRUE(), GAMMADIST returns 0 if x < 0 and the value
otherwise.
See also GAMMAINV 6.18.32
Summary: returns the inverse of GAMMADIST(x;a;;TRUE()).
Syntax: GAMMAINV( Number p ; Number a ; Number )
Returns: Number
See also GAMMADIST 6.18.31
Summary: Returns 0.5 less than the standard normal cumulative distribution
Syntax: GAUSS( Number x )
Returns: Number
Semantics: Returns NORMDIST(x;0;1;TRUE())0.5
See also NORMDIST 6.18.52
Summary: returns the geometric mean of a sequence
Syntax: GEOMEAN( { NumberSequenceList N }+ )
Returns: Number
Semantics: Returns the geometric mean of a given sequence. That means
where n is a result of calling COUNT(N).
Summary: Returns predicted values based on an exponential regression.
Syntax: GROWTH( Array knownY [ ; [ Array knownX ] [ ; [ Array newX ] [ ; Logical Const = TRUE() ] ] ] )
Returns: Array
Constraints: (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = ROWS(knownX)) or (COLUMNS(knownY) = 1 and ROWS(knownY) = ROWS(knownX) and COLUMNS(knownX) = COLUMNS(newX)) or (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = 1 and ROWS(knownX) = ROWS(newX))
Semantics:
knownY: The set of known yvalues to be used to determine the regression equation
Const: If set to FALSE(), the model constant a is equal to 0.
See also TREND 6.18.79
Summary: returns the harmonic mean of a sequence
Syntax: HARMEAN( { NumberSequenceList N }+ )
Returns: Number
Semantics: Returns the harmonic mean of a given sequence. That means
where a1,a2,...,an are the numbers of the sequence N and n is a result of calling COUNT(N).
Summary: The hypergeometric distribution returns the number of successes in a sequence of n draws from a finite population without replacement.
Syntax: HYPGEOMDIST( Integer x ; Integer n ; Integer M ; Integer N [ ; Logical Cumulative = FALSE() ] )
Returns: Number
Constraints: 0 <= x <= n <= N, 0 <= M <= N
Semantics:
x is the number of successes in n trials
n is the number of trials
M is the number of successes in the population
N is the total population
cumulative is a Logical parameter. If cumulative is FALSE(), return the probability of exactly x successes. If cumulative is TRUE(), return the probability of at most x successes. If omitted, FALSE() is assumed.
If Cumulative is FALSE(), HYPGEOMDIST returns
If Cumulative is TRUE(), HYPGEOMDIST returns
Note:
Summary: Returns the yintercept of the linear regression line for the given data.
Syntax: INTERCEPT( ForceArray Array Data_Y ; ForceArray Array Data_X )
Returns: Number
Constraints: COLUMNS(Data_X) = COLUMNS(Data_Y), ROWS(Data_X) = ROWS(Data_Y)
Semantics:
INTERCEPT returns the intercept (a) calculated as described in 5.18.41 for the function call LINEST(DATA_Y,DATA_X,FALSE()).
For an empty element or an element of type Text or Boolean in Data_Y the element at the corresponding position of Data_X is ignored, and vice versa.
Summary: Return the kurtosis (“peakedness”) of a data set.
Syntax: KURT( { NumberSequenceList X } + )
Returns: Number
Constraints: #Numbers>=4, STDEV(X) <> 0
Semantics:
Kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. Positive kurtosis indicates a relatively peaked distribution (compared to the normal distribution), while negative kurtosis indicates a relatively flat distribution.
where s is the sample standard deviation, and n is the number of numbers.
Summary: Finds the nth largest value in a list.
Syntax: LARGE( NumberSequenceList List ; NumberArray N )
Returns: Number or Array
Constraints: ROUNDUP(N;0)=N. If the resulting N is <1 or larger than the size of List, Error is returned
Semantics: If N is an array of numbers, an array of largest values is returned.
See also SMALL 6.18.70, ROUNDUP 6.17.7
Summary: Returns the parameters of the (simple or multiple) linear regression equation for the given data and, optionally, statistics on this regression.
Syntax: LINEST( Array knownY [ ; [ Array knownX ] [ ; Logical Const = TRUE() [ ; Logical Stats = FALSE() ] ] ] )
Returns: Array
Constraints: (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = ROWS(knownX)) or (COLUMNS(knownY) = 1 and ROWS(knownY) = ROWS(knownX)) or (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = 1)
Semantics:
knownY: The set of yvalues for the equation
Const: If set to FALSE(), the model constant a is equal to 0.
Stats: If FALSE(), only the regression coefficient is to be calculated. If set to TRUE(), the result will include other statistical data.
If any of the entries in knownY and knownX do not convert to Number, LINEST returns an error.
The result created by LINEST if STATS is TRUE() is given in Table 28  LINEST. If STATS is FALSE() it is just the first row of Table 28  LINEST. The empty cells in this table are returned as empty or as containing an error.
Table 28  LINEST
bn  bn1  …  b1  a 
  …   
    
F  df    
SSreg  SSresid    
The statistics in the 2nd to 5th rows of Table 28  LINEST are as follows:
If Const is TRUE():
. , , and where is the element in the ith row and ith column of , , and . If Const is FALSE():
, , , where is the element in the ith row and ith column of , , and . In this case is undefined and is returned as either 0, blank or an error. If
is not invertible, then the columns of X are linearly dependent. In this case an evaluator shall return an error or select any maximal linearly independent subset of these columns that if Const is TRUE() includes the first column and perform the above calculations with that subset. In the latter case the coefficients
of omitted columns are returned as 0.
Summary: Returns the parameters of an exponential regression equation for the given data obtained by linearizing this intrinsically linear response function and returns, optionally, statistics on this regression.
Syntax: LOGEST( Array knownY [ ; [ Array knownX ] [ ; Logical Const = TRUE() [ ; Logical Stats = FALSE() ] ] ] )
Returns: Array
Constraints: (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = ROWS(knownX)) or (COLUMNS(knownY) = 1 and ROWS(knownY) = ROWS(knownX)) or (COLUMNS(knownY) = COLUMNS(knownX) and ROWS(knownY) = 1)
Semantics:
knownY: The set of yvalues for the equation
Const: If set to FALSE(), the model constant a is equal to 0.
Stats: If FALSE(), only the regression coefficient is to be calculated. If set to TRUE(), the result will include other statistical data.
If any of the entries in knownY and knownX do not convert to Number or if any of the entries in knownY is negative, LOGEST returns an error.
The result created by LOGEST if STATS is TRUE() is given in Table 29  LOGEST. If STATS is FALSE() it is just the first row of Table 29  LOGEST. The empty cells in this table are returned as empty or as containing an error.
Table 29  LOGEST