# Mathematics

• ABS absolute value
• ACOS the arc cosine of x
• ACOSH the hyperbolic arc cosine of x
• ACOT inverse cotangent of x
• ACOTH the inverse hyperbolic cotangent of x
• AGM the arithmetic-geometric mean
• ARABIC the Roman numeral roman as number
• ASIN the arc sine of x
• ASINH the inverse hyperbolic sine of x
• ATAN the arc tangent of x
• ATAN2 the arc tangent of the ratio y/x
• ATANH the inverse hyperbolic tangent of x
• AVERAGEIF average of the cells in actual range for which the corresponding cells in the range meet the given criteria
• AVERAGEIFS average of the cells in actual_range for which the corresponding cells in the range meet the given criteria
• BETA Euler beta function
• BETALN natural logarithm of the absolute value of the Euler beta function
• CEIL smallest integer larger than or equal to x
• CEILING nearest multiple of significance whose absolute value is at least ABS(x)
• CHOLESKY the Cholesky decomposition of the symmetric positive-definite matrix
• COMBIN binomial coefficient
• COMBINA the number of k-combinations of an n-element set with repetition
• COS the cosine of x
• COSH the hyperbolic cosine of x
• COSPI the cosine of Pi*x
• COT the cotangent of x
• COTH the hyperbolic cotangent of x
• COTPI the cotangent of Pi*x
• COUNTIF count of the cells meeting the given criteria
• COUNTIFS count of the cells meeting the given criteria
• CSC the cosecant of x
• CSCH the hyperbolic cosecant of x
• DEGREES equivalent degrees to x radians
• EIGEN eigenvalues and eigenvectors of the symmetric matrix
• EVEN x rounded away from 0 to the next even integer
• EXP e raised to the power of x
• EXPM1 EXP(x)-1
• FACT the factorial of x, i.e. x!
• FACTDOUBLE double factorial
• FIB Fibonacci numbers
• FLOOR nearest multiple of significance whose absolute value is at most ABS(x)
• G_PRODUCT product of all the values and cells referenced
• GAMMA the Gamma function
• GAMMALN natural logarithm of the Gamma function
• GCD the greatest common divisor
• GD Gudermannian function
• HYPOT the square root of the sum of the squares of the arguments
• IGAMMA the incomplete Gamma function
• INT largest integer not larger than x
• LAMBERTW the Lambert W function
• LCM the least common multiple
• LINSOLVE solve linear equation
• LN the natural logarithm of x
• LN1P LN(1+x)
• LOG logarithm of x with base base
• LOG10 the base-10 logarithm of x
• LOG2 the base-2 logarithm of x
• MAXIFS maximum of the cells in actual_range for which the corresponding cells in the range meet the given criteria
• MDETERM the determinant of the matrix matrix
• MINIFS minimum of the cells in actual_range for which the corresponding cells in the range meet the given criteria
• MINVERSE the inverse matrix of matrix
• MMULT the matrix product of mat1 and mat2
• MOD the remainder of x under division by n
• MPSEUDOINVERSE the pseudo-inverse matrix of matrix
• MROUND x rounded to a multiple of m
• MULTINOMIAL multinomial coefficient (x1+⋯+xn) choose (x1,…,xn)
• MUNIT the n by n identity matrix
• ODD x rounded away from 0 to the next odd integer
• ODF.SUMPRODUCT multiplies components and adds the results
• PI the constant 𝜋
• POCHHAMMER the value of GAMMA(x+n)/GAMMA(x)
• POWER the value of x raised to the power y raised to the power of 1/z
• PRODUCT product of the given values
• QUOTIENT integer portion of a division
• RADIANS the number of radians equivalent to x degrees
• REDUCEPI reduce modulo Pi divided by a power of 2
• ROMAN n as a roman numeral text
• ROUND rounded x
• ROUNDDOWN x rounded towards 0
• ROUNDUP x rounded away from 0
• SEC Secant
• SECH the hyperbolic secant of x
• SERIESSUM sum of a power series at x
• SIGN sign of x
• SIN the sine of x
• SINH the hyperbolic sine of x
• SINPI the sine of Pi*x
• SQRT square root of x
• SQRTPI the square root of x times 𝜋
• SUM sum of the given values
• SUMA sum of all values and cells referenced
• SUMIF sum of the cells in actual_range for which the corresponding cells in the range meet the given criteria
• SUMIFS sum of the cells in actual_range for which the corresponding cells in the range meet the given criteria
• SUMPRODUCT multiplies components and adds the results
• SUMSQ sum of the squares of all values and cells referenced
• SUMX2MY2 sum of the difference of squares
• SUMX2PY2 sum of the sum of squares
• SUMXMY2 sum of the squares of differences
• TAN the tangent of x
• TANH the hyperbolic tangent of x
• TANPI the tangent of Pi*x
• TRUNC x truncated to d digits

## ABS

ABS absolute value

`ABS(x)`

x: number

### Description

ABS gives the absolute value of x, i.e. the non-negative number of the same magnitude as x.

### Microsoft Excel Compatibility

This function is Excel compatible.

## ACOS

ACOS the arc cosine of x

### Synopsis

`ACOS(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

## ACOSH

ACOSH the hyperbolic arc cosine of x

### Synopsis

`ACOSH(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

## ACOT

ACOT inverse cotangent of x

### Synopsis

`ACOT(x)`

x: value

COT, TAN.

## ACOTH

ACOTH the inverse hyperbolic cotangent of x

### Synopsis

`ACOTH(x)`

x: number

COTH, TANH.

## AGM

AGM the arithmetic-geometric mean

### Synopsis

`AGM(a,b)`

a: value

b: value

### Description

AGM computes the arithmetic-geometric mean of the two values.

## ARABIC

ARABIC the Roman numeral roman as number

### Synopsis

`ARABIC(roman)`

### Arguments

roman: Roman numeral

### Description

Any Roman symbol to the left of a larger symbol (directly or indirectly) reduces the final value by the symbol amount, otherwise, it increases the final amount by the symbol's amount.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## ASIN

ASIN the arc sine of x

### Synopsis

`ASIN(x)`

x: number

### Description

ASIN calculates the arc sine of x; that is the value whose sine is x.

### Note

If x falls outside the range -1 to 1, ASIN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## ASINH

ASINH the inverse hyperbolic sine of x

### Synopsis

`ASINH(x)`

x: number

### Description

ASINH calculates the inverse hyperbolic sine of x; that is the value whose hyperbolic sine is x.

### Microsoft Excel Compatibility

This function is Excel compatible.

ASIN, ACOSH, SIN, COS.

## ATAN

ATAN the arc tangent of x

### Synopsis

`ATAN(x)`

x: number

### Description

ATAN calculates the arc tangent of x; that is the value whose tangent is x.

### Note

The result will be between −π/2 and +π/2.

### Microsoft Excel Compatibility

This function is Excel compatible.

## ATAN2

ATAN2 the arc tangent of the ratio y/x

### Synopsis

`ATAN2(x,y)`

x: x-coordinate

y: y-coordinate

### Description

ATAN2 calculates the direction from the origin to the point (x,y) as an angle from the x-axis in radians.

### Note

The result will be between −π and +π. The order of the arguments may be unexpected.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

ATAN, ATANH, COS, SIN.

## ATANH

ATANH the inverse hyperbolic tangent of x

### Synopsis

`ATANH(x)`

x: number

### Description

ATANH calculates the inverse hyperbolic tangent of x; that is the value whose hyperbolic tangent is x.

### Note

If the absolute value of x is greater than 1.0, ATANH returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

ATAN, COS, SIN.

## AVERAGEIF

AVERAGEIF average of the cells in actual range for which the corresponding cells in the range meet the given criteria

### Synopsis

`AVERAGEIF(range,criteria,actual_range)`

### Arguments

range: cell area

criteria: condition for a cell to be included

actual_range: cell area, defaults to range

### Microsoft Excel Compatibility

This function is Excel compatible.

## AVERAGEIFS

AVERAGEIFS average of the cells in actual_range for which the corresponding cells in the range meet the given criteria

### Synopsis

`AVERAGEIFS(actual_range,range1,criteria1,…)`

### Arguments

actual_range: cell area

range1: cell area

criteria1: condition for a cell to be included

### Microsoft Excel Compatibility

This function is Excel compatible.

## BETA

BETA Euler beta function

### Synopsis

`BETA(x,y)`

x: number

y: number

### Description

BETA function returns the value of the Euler beta function extended to all real numbers except 0 and negative integers.

### Note

If x, y, or (x + y) are non-positive integers, BETA returns #NUM!

## BETALN

BETALN natural logarithm of the absolute value of the Euler beta function

### Synopsis

`BETALN(x,y)`

x: number

y: number

### Description

BETALN function returns the natural logarithm of the absolute value of the Euler beta function extended to all real numbers except 0 and negative integers.

### Note

If x, y, or (x + y) are non-positive integers, BETALN returns #NUM!

## CEIL

CEIL smallest integer larger than or equal to x

### Synopsis

`CEIL(x)`

x: number

### Description

CEIL(x) is the smallest integer that is at least as large as x.

### OpenDocument Format (ODF) Compatibility

This function is the OpenFormula function CEILING(x).

## CEILING

CEILING nearest multiple of significance whose absolute value is at least ABS(x)

### Synopsis

`CEILING(x,significance)`

### Arguments

x: number

significance: base multiple (defaults to 1 for x > 0 and -1 for x < 0)

### Description

CEILING(x,significance) is the nearest multiple of significance whose absolute value is at least ABS(x).

### Note

If x or significance is non-numeric, CEILING returns a #VALUE! error. If x and significance have different signs, CEILING returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

CEILING(x) is exported to ODF as CEILING(x,SIGN(x),1). CEILING(x,significance) is the OpenFormula function CEILING(x,significance,1).

CEIL, FLOOR, ABS, INT, MOD.

## CHOLESKY

CHOLESKY the Cholesky decomposition of the symmetric positive-definite matrix

### Synopsis

`CHOLESKY(matrix)`

### Arguments

matrix: a symmetric positive definite matrix

### Note

If the Cholesky-Banachiewicz algorithm applied to matrix fails, Cholesky returns #NUM! If matrix does not contain an equal number of columns and rows, CHOLESKY returns #VALUE!

## COMBIN

COMBIN binomial coefficient

### Synopsis

`COMBIN(n,k)`

### Arguments

n: non-negative integer

k: non-negative integer

### Description

COMBIN returns the binomial coefficient "n choose k", the number of k-combinations of an n-element set without repetition.

### Note

If n is less than k COMBIN returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## COMBINA

COMBINA the number of k-combinations of an n-element set with repetition

### Synopsis

`COMBINA(n,k)`

### Arguments

n: non-negative integer

k: non-negative integer

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## COS

COS the cosine of x

`COS(x)`

### Arguments

x: angle in radians

### Description

This function is Excel compatible.

## COSH

COSH the hyperbolic cosine of x

### Synopsis

`COSH(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

SIN, TAN, SINH, COSH, TANH.

## COSPI

COSPI the cosine of Pi*x

### Synopsis

`COSPI(x)`

### Arguments

x: number of half turns

COS.

## COT

COT the cotangent of x

`COT(x)`

x: number

TAN, ACOT.

## COTH

COTH the hyperbolic cotangent of x

### Synopsis

`COTH(x)`

x: number

## COTPI

COTPI the cotangent of Pi*x

### Synopsis

`COTPI(x)`

### Arguments

x: number of half turns

COT.

## COUNTIF

COUNTIF count of the cells meeting the given criteria

### Synopsis

`COUNTIF(range,criteria)`

### Arguments

range: cell area

criteria: condition for a cell to be counted

### Microsoft Excel Compatibility

This function is Excel compatible.

## COUNTIFS

COUNTIFS count of the cells meeting the given criteria

### Synopsis

`COUNTIFS(range,criteria,…)`

### Arguments

range: cell area

criteria: condition for a cell to be counted

### Microsoft Excel Compatibility

This function is Excel compatible.

## CSC

CSC the cosecant of x

`CSC(x)`

### Arguments

x: angle in radians

### Microsoft Excel Compatibility

This function is not Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## CSCH

CSCH the hyperbolic cosecant of x

### Synopsis

`CSCH(x)`

x: number

### Microsoft Excel Compatibility

This function is not Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

SIN, COS, TAN, CSC, SEC, SINH, COSH, TANH.

## DEGREES

DEGREES equivalent degrees to x radians

### Synopsis

`DEGREES(x)`

### Arguments

x: angle in radians

### Microsoft Excel Compatibility

This function is Excel compatible.

## EIGEN

EIGEN eigenvalues and eigenvectors of the symmetric matrix

### Synopsis

`EIGEN(matrix)`

### Arguments

matrix: a symmetric matrix

### Note

If matrix is not symmetric, matching off-diagonal cells will be averaged on the assumption that the non-symmetry is caused by unimportant rounding errors. If matrix does not contain an equal number of columns and rows, EIGEN returns #VALUE!

## EVEN

EVEN x rounded away from 0 to the next even integer

### Synopsis

`EVEN(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

ODD.

## EXP

EXP e raised to the power of x

`EXP(x)`

x: number

### Note

e is the base of the natural logarithm.

### Microsoft Excel Compatibility

This function is Excel compatible.

LOG, LOG2, LOG10.

## EXPM1

EXPM1 EXP(x)-1

### Synopsis

`EXPM1(x)`

x: number

### Note

This function has a higher resulting precision than evaluating EXP(x)-1.

EXP, LN1P.

## FACT

FACT the factorial of x, i.e. x!

### Synopsis

`FACT(x)`

x: number

### Note

The domain of this function has been extended using the GAMMA function.

### Microsoft Excel Compatibility

This function is Excel compatible.

## FACTDOUBLE

FACTDOUBLE double factorial

### Synopsis

`FACTDOUBLE(x)`

### Arguments

x: non-negative integer

### Description

FACTDOUBLE function returns the double factorial x!!

### Note

If x is not an integer, it is truncated. If x is negative, FACTDOUBLE returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

FACT.

## FIB

FIB Fibonacci numbers

`FIB(n)`

### Arguments

n: positive integer

### Description

FIB(n) is the nth Fibonacci number.

### Note

If n is not an integer, it is truncated. If it is negative or zero FIB returns #NUM!

## FLOOR

FLOOR nearest multiple of significance whose absolute value is at most ABS(x)

### Synopsis

`FLOOR(x,significance)`

### Arguments

x: number

significance: base multiple (defaults to 1 for x > 0 and -1 for x < 0)

### Description

FLOOR(x,significance) is the nearest multiple of significance whose absolute value is at most ABS(x)

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

FLOOR(x) is exported to ODF as FLOOR(x,SIGN(x),1). FLOOR(x,significance) is the OpenFormula function FLOOR(x,significance,1).

CEIL, CEILING, ABS, INT, MOD.

## G_PRODUCT

G_PRODUCT product of all the values and cells referenced

### Synopsis

`G_PRODUCT(x1,x2,…)`

x1: number

x2: number

### Note

Empty cells are ignored and the empty product is 1.

SUM, COUNT.

## GAMMA

GAMMA the Gamma function

### Synopsis

`GAMMA(x)`

x: number

## GAMMALN

GAMMALN natural logarithm of the Gamma function

### Synopsis

`GAMMALN(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

## GCD

GCD the greatest common divisor

### Synopsis

`GCD(n0,n1,…)`

### Arguments

n0: positive integer

n1: positive integer

### Description

GCD calculates the greatest common divisor of the given numbers n0,n1,..., the greatest integer that is a divisor of each argument.

### Note

If any of the arguments is not an integer, it is truncated.

### Microsoft Excel Compatibility

This function is Excel compatible.

LCM.

## GD

GD Gudermannian function

`GD(x)`

x: value

TAN, TANH.

## HYPOT

HYPOT the square root of the sum of the squares of the arguments

### Synopsis

`HYPOT(n0,n1,…)`

n0: number

n1: number

MIN, MAX.

## IGAMMA

IGAMMA the incomplete Gamma function

### Synopsis

`IGAMMA(a,x,lower,regularize,real)`

### Arguments

a: number

x: number

lower: if true (the default), the lower incomplete gamma function, otherwise the upper incomplete gamma function

regularize: if true (the default), the regularized version of the incomplete gamma function

real: if true (the default), the real part of the result, otherwise the imaginary part

### Note

The regularized incomplete gamma function is the unregularized incomplete gamma function divided by GAMMA(a) This is a real valued function as long as neither a nor z are negative.

## INT

INT largest integer not larger than x

`INT(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

## LAMBERTW

LAMBERTW the Lambert W function

### Synopsis

`LAMBERTW(x,k)`

x: number

k: branch

### Note

k defaults to 0, the principal branch. k must be either 0 or -1.

EXP.

## LCM

LCM the least common multiple

### Synopsis

`LCM(n0,n1,…)`

### Arguments

n0: positive integer

n1: positive integer

### Description

LCM calculates the least common multiple of the given numbers n0,n1,..., the smallest integer that is a multiple of each argument.

### Note

If any of the arguments is not an integer, it is truncated.

### Microsoft Excel Compatibility

This function is Excel compatible.

GCD.

## LINSOLVE

LINSOLVE solve linear equation

### Synopsis

`LINSOLVE(A,B)`

A: a matrix

B: a matrix

### Description

Solves the equation A*X=B and returns X.

### Note

If the matrix A is singular, #VALUE! is returned.

## LN

LN the natural logarithm of x

`LN(x)`

### Arguments

x: positive number

### Note

If x ≤ 0, LN returns #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

EXP, LOG2, LOG10.

## LN1P

LN1P LN(1+x)

### Synopsis

`LN1P(x)`

### Arguments

x: positive number

### Description

LN1P calculates LN(1+x) but yielding a higher precision than evaluating LN(1+x).

### Note

If x ≤ -1, LN returns #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

EXP, LN, EXPM1.

## LOG

LOG logarithm of x with base base

### Synopsis

`LOG(x,base)`

### Arguments

x: positive number

base: base of the logarithm, defaults to 10

### Note

base must be positive and not equal to 1. If x ≤ 0, LOG returns #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

LN, LOG2, LOG10.

## LOG10

LOG10 the base-10 logarithm of x

### Synopsis

`LOG10(x)`

### Arguments

x: positive number

### Note

If x ≤ 0, LOG10 returns #NUM!

EXP, LOG2, LOG.

## LOG2

LOG2 the base-2 logarithm of x

### Synopsis

`LOG2(x)`

### Arguments

x: positive number

### Note

If x ≤ 0, LOG2 returns #NUM!

EXP, LOG10, LOG.

## MAXIFS

MAXIFS maximum of the cells in actual_range for which the corresponding cells in the range meet the given criteria

### Synopsis

`MAXIFS(actual_range,range1,criteria1,…)`

### Arguments

actual_range: cell area

range1: cell area

criteria1: condition for a cell to be included

### Microsoft Excel Compatibility

This function is Excel compatible.

## MDETERM

MDETERM the determinant of the matrix matrix

### Synopsis

`MDETERM(matrix)`

### Arguments

matrix: a square matrix

### Microsoft Excel Compatibility

This function is Excel compatible.

## MINIFS

MINIFS minimum of the cells in actual_range for which the corresponding cells in the range meet the given criteria

### Synopsis

`MINIFS(actual_range,range1,criteria1,…)`

### Arguments

actual_range: cell area

range1: cell area

criteria1: condition for a cell to be included

### Microsoft Excel Compatibility

This function is Excel compatible.

## MINVERSE

MINVERSE the inverse matrix of matrix

### Synopsis

`MINVERSE(matrix)`

### Arguments

matrix: a square matrix

### Note

If matrix is not invertible, MINVERSE returns #NUM! If matrix does not contain an equal number of columns and rows, MINVERSE returns #VALUE!

### Microsoft Excel Compatibility

This function is Excel compatible.

## MMULT

MMULT the matrix product of mat1 and mat2

### Synopsis

`MMULT(mat1,mat2)`

mat1: a matrix

mat2: a matrix

### Note

The number of columns in mat1 must equal the number of rows in mat2; otherwise #VALUE! is returned. The result of MMULT is an array, in which the number of rows is the same as in mat1), and the number of columns is the same as in (mat2).

### Microsoft Excel Compatibility

This function is Excel compatible.

## MOD

MOD the remainder of x under division by n

### Synopsis

`MOD(x,n)`

x: integer

n: integer

### Description

MOD function returns the remainder when x is divided by n.

### Note

If n is 0, MOD returns #DIV/0!

### Microsoft Excel Compatibility

This function is Excel compatible.

## MPSEUDOINVERSE

MPSEUDOINVERSE the pseudo-inverse matrix of matrix

### Synopsis

`MPSEUDOINVERSE(matrix,threshold)`

### Arguments

matrix: a matrix

threshold: a relative size threshold for discarding eigenvalues

## MROUND

MROUND x rounded to a multiple of m

### Synopsis

`MROUND(x,m)`

x: number

m: number

### Note

If x and m have different sign, MROUND returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## MULTINOMIAL

MULTINOMIAL multinomial coefficient (x1+⋯+xn) choose (x1,…,xn)

### Synopsis

`MULTINOMIAL(x1,x2,xn,…)`

### Arguments

x1: first number

x2: second number

xn: nth number

### Microsoft Excel Compatibility

This function is Excel compatible.

## MUNIT

MUNIT the n by n identity matrix

### Synopsis

`MUNIT(n)`

### Arguments

n: size of the matrix

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## ODD

ODD x rounded away from 0 to the next odd integer

`ODD(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

EVEN.

## ODF.SUMPRODUCT

ODF.SUMPRODUCT multiplies components and adds the results

### Synopsis

`ODF.SUMPRODUCT(,…)`

### Description

Multiplies corresponding data entries in the given arrays or ranges, and then returns the sum of those products.

### Note

If an entry is not numeric or logical, the value zero is used instead. If arrays or range arguments do not have the same dimensions, return #VALUE! error. This function differs from SUMPRODUCT by considering booleans.

### Microsoft Excel Compatibility

This function is not Excel compatible. Use SUMPRODUCT instead.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## PI

PI the constant 𝜋

`PI()`

### Microsoft Excel Compatibility

This function is Excel compatible, but it returns 𝜋 with a better precision.

## POCHHAMMER

POCHHAMMER the value of GAMMA(x+n)/GAMMA(x)

### Synopsis

`POCHHAMMER(x,n)`

x: number

n: number

## POWER

POWER the value of x raised to the power y raised to the power of 1/z

### Synopsis

`POWER(x,y,z)`

x: number

y: number

z: number

### Note

If both x and y equal 0, POWER returns #NUM! If x = 0 and y < 0, POWER returns #DIV/0! If x < 0 and y is not an integer, POWER returns #NUM! z defaults to 1 If z is not a positive integer, POWER returns #NUM! If x < 0, y is odd, and z is even, POWER returns #NUM!

EXP.

## PRODUCT

PRODUCT product of the given values

### Synopsis

`PRODUCT(values,…)`

### Arguments

values: a list of values to multiply

### Description

PRODUCT computes the product of all the values and cells referenced in the argument list.

### Note

If all cells are empty, the result will be 0.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## QUOTIENT

QUOTIENT integer portion of a division

### Synopsis

`QUOTIENT(numerator,denominator)`

### Arguments

numerator: integer

denominator: non-zero integer

### Description

QUOTIENT yields the integer portion of the division numerator/denominator.

QUOTIENT (numerator,denominator)⨉denominator+MOD(numerator,denominator)=numerator

### Microsoft Excel Compatibility

This function is Excel compatible.

MOD.

RADIANS the number of radians equivalent to x degrees

### Synopsis

`RADIANS(x)`

### Arguments

x: angle in degrees

### Microsoft Excel Compatibility

This function is Excel compatible.

## REDUCEPI

REDUCEPI reduce modulo Pi divided by a power of 2

### Synopsis

`REDUCEPI(x,e,q)`

### Arguments

x: number

e: scale

q: get lower bits of quotient, defaults to FALSE

### Note

This function returns a value, xr, such that x=xr+j*Pi/2^e where j is an integer and the absolute value of xr does not exceed Pi/2^(e+1). If optional argument q is TRUE, returns instead the e+1 lower bits of j. The reduction is performed as-if using an exact value of Pi. The lowest valid e is -1 representing reduction modulo 2*Pi; the highest is 7 representing reduction modulo Pi/256.

PI.

## ROMAN

ROMAN n as a roman numeral text

### Synopsis

`ROMAN(n,type)`

### Arguments

n: non-negative integer

type: 0,1,2,3,or 4, defaults to 0

### Description

ROMAN returns the arabic number n as a roman numeral text.

If type is 0 or it is omitted, ROMAN returns classic roman numbers.

Type 1 is more concise than classic type, type 2 is more concise than type 1, and type 3 is more concise than type 2. Type 4 is a simplified type.

### Microsoft Excel Compatibility

This function is Excel compatible.

## ROUND

ROUND rounded x

### Synopsis

`ROUND(x,d)`

### Arguments

x: number

d: integer, defaults to 0

### Description

If d is greater than zero, x is rounded to the given number of digits.

If d is zero, x is rounded to the next integer.

If d is less than zero, x is rounded to the left of the decimal point

### Microsoft Excel Compatibility

This function is Excel compatible.

## ROUNDDOWN

ROUNDDOWN x rounded towards 0

### Synopsis

`ROUNDDOWN(x,d)`

### Arguments

x: number

d: integer, defaults to 0

### Description

If d is greater than zero, x is rounded toward 0 to the given number of digits.

If d is zero, x is rounded toward 0 to the next integer.

If d is less than zero, x is rounded toward 0 to the left of the decimal point

### Microsoft Excel Compatibility

This function is Excel compatible.

## ROUNDUP

ROUNDUP x rounded away from 0

### Synopsis

`ROUNDUP(x,d)`

### Arguments

x: number

d: integer, defaults to 0

### Description

If d is greater than zero, x is rounded away from 0 to the given number of digits.

If d is zero, x is rounded away from 0 to the next integer.

If d is less than zero, x is rounded away from 0 to the left of the decimal point

### Microsoft Excel Compatibility

This function is Excel compatible.

## SEC

SEC Secant

`SEC(x)`

### Arguments

x: angle in radians

### Microsoft Excel Compatibility

This function is not Excel compatible.

### OpenDocument Format (ODF) Compatibility

SEC(x) is exported to OpenFormula as 1/COS(x).

## SECH

SECH the hyperbolic secant of x

### Synopsis

`SECH(x)`

x: number

### Microsoft Excel Compatibility

This function is not Excel compatible.

### OpenDocument Format (ODF) Compatibility

SECH(x) is exported to OpenFormula as 1/COSH(x).

SIN, COS, TAN, CSC, SEC, SINH, COSH, TANH.

## SERIESSUM

SERIESSUM sum of a power series at x

### Synopsis

`SERIESSUM(x,n,m,coeff)`

### Arguments

x: number where to evaluate the power series

n: non-negative integer, exponent of the lowest term of the series

m: increment to each exponent

coeff: coefficients of the power series

### Microsoft Excel Compatibility

This function is Excel compatible.

COUNT, SUM.

## SIGN

SIGN sign of x

### Synopsis

`SIGN(x)`

x: number

### Description

SIGN returns 1 if the x is positive and it returns -1 if x is negative.

### Microsoft Excel Compatibility

This function is Excel compatible.

ABS.

## SIN

SIN the sine of x

`SIN(x)`

### Arguments

x: angle in radians

### Microsoft Excel Compatibility

This function is Excel compatible.

## SINH

SINH the hyperbolic sine of x

### Synopsis

`SINH(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

SIN, COSH, ASINH.

## SINPI

SINPI the sine of Pi*x

### Synopsis

`SINPI(x)`

### Arguments

x: number of half turns

SIN.

## SQRT

SQRT square root of x

### Synopsis

`SQRT(x)`

### Arguments

x: non-negative number

### Note

If x is negative, SQRT returns #NUM!

### Microsoft Excel Compatibility

This function is Excel compatible.

## SQRTPI

SQRTPI the square root of x times 𝜋

### Synopsis

`SQRTPI(x)`

### Arguments

x: non-negative number

### Microsoft Excel Compatibility

This function is Excel compatible.

PI.

## SUM

SUM sum of the given values

### Synopsis

`SUM(values,…)`

### Arguments

values: a list of values to add

### Description

SUM computes the sum of all the values and cells referenced in the argument list.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## SUMA

SUMA sum of all values and cells referenced

### Synopsis

`SUMA(area0,area1,…)`

### Arguments

area0: first cell area

area1: second cell area

### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1).

## SUMIF

SUMIF sum of the cells in actual_range for which the corresponding cells in the range meet the given criteria

### Synopsis

`SUMIF(range,criteria,actual_range)`

### Arguments

range: cell area

criteria: condition for a cell to be summed

actual_range: cell area, defaults to range

### Note

If the actual_range has a size that differs from the size of range, actual_range is resized (retaining the top-left corner) to match the size of range.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SUMIFS

SUMIFS sum of the cells in actual_range for which the corresponding cells in the range meet the given criteria

### Synopsis

`SUMIFS(actual_range,range1,criteria1,…)`

### Arguments

actual_range: cell area

range1: cell area

criteria1: condition for a cell to be included

### Microsoft Excel Compatibility

This function is Excel compatible.

SUM, SUMIF.

## SUMPRODUCT

SUMPRODUCT multiplies components and adds the results

### Synopsis

`SUMPRODUCT(,…)`

### Description

Multiplies corresponding data entries in the given arrays or ranges, and then returns the sum of those products.

### Note

If an entry is not numeric, the value zero is used instead. If arrays or range arguments do not have the same dimensions, return #VALUE! error. This function ignores logicals, so using SUMPRODUCT(A1:A5>0) will not work. Instead use SUMPRODUCT(--(A1:A5>0))

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is not OpenFormula compatible. Use ODF.SUMPRODUCT instead.

## SUMSQ

SUMSQ sum of the squares of all values and cells referenced

### Synopsis

`SUMSQ(area0,area1,…)`

### Arguments

area0: first cell area

area1: second cell area

### Microsoft Excel Compatibility

This function is Excel compatible.

SUM, COUNT.

## SUMX2MY2

SUMX2MY2 sum of the difference of squares

### Synopsis

`SUMX2MY2(array0,array1)`

### Arguments

array0: first cell area

array1: second cell area

### Description

SUMX2MY2 function returns the sum of the difference of squares of corresponding values in two arrays. The equation of SUMX2MY2 is SUM(x^2-y^2).

### Microsoft Excel Compatibility

This function is Excel compatible.

## SUMX2PY2

SUMX2PY2 sum of the sum of squares

### Synopsis

`SUMX2PY2(array0,array1)`

### Arguments

array0: first cell area

array1: second cell area

### Description

SUMX2PY2 function returns the sum of the sum of squares of corresponding values in two arrays. The equation of SUMX2PY2 is SUM(x^2+y^2).

### Note

If array0 and array1 have different number of data points, SUMX2PY2 returns #N/A.

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SUMXMY2

SUMXMY2 sum of the squares of differences

### Synopsis

`SUMXMY2(array0,array1)`

### Arguments

array0: first cell area

array1: second cell area

### Description

SUMXMY2 function returns the sum of the squares of the differences of corresponding values in two arrays. The equation of SUMXMY2 is SUM((x-y)^2).

### Note

If array0 and array1 have different number of data points, SUMXMY2 returns #N/A.

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## TAN

TAN the tangent of x

`TAN(x)`

### Arguments

x: angle in radians

### Microsoft Excel Compatibility

This function is Excel compatible.

## TANH

TANH the hyperbolic tangent of x

### Synopsis

`TANH(x)`

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

TAN, SIN, SINH, COS, COSH.

## TANPI

TANPI the tangent of Pi*x

### Synopsis

`TANPI(x)`

### Arguments

x: number of half turns

TAN.

## TRUNC

TRUNC x truncated to d digits

### Synopsis

`TRUNC(x,d)`

### Arguments

x: number

d: non-negative integer, defaults to 0

### Note

If d is omitted or negative then it defaults to zero. If it is not an integer then it is truncated to an integer.

### Microsoft Excel Compatibility

This function is Excel compatible.