# Math & Trigonometry Functions

Basic Numeric Information. Conditional Sums. Basic & Advanced Mathematical Operations. Trigonometry. Rounding Functions. Logarithms. Factorials. Matrix Functions.
• ABS

Returns the absolute value of a number.

ABS(-2)
 value (number) The number of which to return the absolute value.
• ACOS

The ACOS function returns the inverse cosine of a value in radians.

ACOS(1)
 value (number) The value for which to calculate the inverse cosine. Must be between -1 and 1, inclusive.
• ACOSH

The ACOSH function returns the inverse hyperbolic cosine of a number.

ACOSH(2)
 value (number) The value for which to calculate the inverse hyperbolic cosine. Must be greater than or equal to 1.
• ACOT

The ACOT function returns the inverse cotangent of a value in radians.

ACOT(-1)
 value (number) The value for which to calculate the inverse cotangent. Values must be a number.
• ACOTH

The ACOTH function returns the inverse hyperbolic cotangent of a value in radians.

ACOTH(10)
 value (number) The value for which to calculate the inverse hyperbolic cotangent.

 value1 (number) Summand 1 value2 (number) Summand 2
• ARABIC

Converts a Roman number to Arabic, as a number

ARABIC("VII")
 roman_text (string) The Roman numeral in text that you want to convert.
• ASIN

The ASIN function returns the inverse sine of a value in radians.

ASIN(1)
 value (number) The value for which to calculate the inverse sine. Must be between -1 and 1, inclusive.
• ASINH

The ASINH function returns the inverse hyperbolic sine of a number.

ASINH(0.9)
 value (number) The value for which to calculate the inverse hyperbolic sine.
• ATAN

The ATAN function returns the inverse tangent of a value in radians.

ATAN(0)
 value (number) The value for which to calculate the inverse tangent.
• ATAN2

The ATAN2 function returns the angle between the x-axis and a line segment from the origin (0,0) to the specified coordinate pair (`x`,`y`), in radians.

ATAN2(4,3)
 x (number) The x coordinate of the endpoint of the line segment for which to calculate the angle from the x-axis. y (number) The y coordinate of the endpoint of the line segment for which to calculate the angle from the x-axis.
• ATANH

The ATANH function returns the inverse hyperbolic tangent of a number.

ATANH(0.9)
 value (number) The value for which to calculate the inverse hyperbolic tangent. Must be between -1 and 1, exclusive.
• BESSELI

Calculates the modified Bessel functions

BESSELI(4.5,1)
 x (number) The value at which the function is to be evaluated. n (number) A positive integer, representing the order of the function.
• BESSELJ

Returns the Bessel function

BESSELJ(2.5,1)
 x (number) The value at which the function is to be evaluated. n (number) The order of the Bessel function (must be a positive integer).
• BESSELK

Calculates the modified Bessel functions. Kn(x), which are also known as the hyperbolic Bessel Functions

BESSELK(0.05,1)
 x (number) The value at which the function is to be evaluated. n (number) A positive integer, denoting the order of the modified Bessel function.
• BESSELY

Returns the Bessel function, Yn(x), (also known as the Weber function or the Neumann function), for a specified order and value of x.

BESSELY(0.05,1)
 x (number) The value at which the function is to be evaluated. n (number) A positive integer, denoting the order of the Bessel function.
• CEIL

Round fractions up

CEIL(4.3)
 value (number) The value to round
• CEILING

The CEILING function rounds a number up to the nearest integer multiple of specified significance.

CEILING(23.25,0.1)
 value (number) The value to round up to the nearest integer multiple of factor. factor (number) Optional: The number to whose multiples value will be rounded - may not be equal to 0.
• CEILING_MATH

Rounds a number up, to the nearest integer or to the nearest multiple of significance

CEILING_MATH(6.3)
 number (number) The number that should be rounded.
• CEILING_PRECISE

Rounds a number the nearest integer or to the nearest multiple of significance. Regardless of the sign of the number, the number is rounded up.

CEILING_PRECISE(-6.3)
 number (number) The number that should be rounded.
• COMBIN

The COMBIN function returns the number of ways to choose some number of objects from a pool of a given size of objects.

COMBIN(4,2)
 n (number) The size of the pool of objects to choose from. k (number) The number of objects to choose.
• COS

The COS function returns the cosine of an angle provided in radians.

COS(1)
 angle (number) The angle to find the cosine of, in radians.
• COSH

The COSH function returns the hyperbolic cosine of any real number.

COSH(1)
 value (number) Any real value to calculate the hyperbolic cosine of.
• COT

The COT function returns the cotangent of an angle provided in radians.

COT(3.14)
 angle (number) The angle to find the cotangent of, in radians.
• COTH

The COTH function returns the hyperbolic cotangent of any real number.

COTH(1)
 value (number) Any real value to calculate the hyperbolic cotangent of.
• COUNTIFS

Returns the count of a range depending on multiple criteria.

COUNTIFS({var1}, ">20", {var2}, "<30")
 criteria_range1 (array) The range to check against criterion1. criterion1 (string) The pattern or test to apply to criteria_range1.
• CSC

The CSC function returns the cosecant of an angle provided in radians.

CSC(1)
 angle (number) Any real value to calculate the cosecant of.
• CSCH

The CSCH function returns the hyperbolic cosecant of any real number.

CSCH(1)
 value (number) Any real value to calculate the hyperbolic cosecant of.

Converts the number in degrees to the radian equivalent

 number (number) Angular value in degrees
• DEGREES

The DEGREES function converts an angle value in radians to degrees.

DEGREES(6)
 angle (number) The angle to convert from radians to degrees.
• DIVIDE

Divide number

DIVIDE(4,2)
 divisible (number) Divisible divider (number) Divider
• ERFC_PRECISE

Returns the complementary Gauss error function of a value.

ERFC_PRECISE(2)
 z (number) The number for which to calculate the complementary Gauss error function.
• EVEN

Rounds a number up to the nearest even integer.

EVEN(-0.6)
 value (number) The value to round to the next greatest even number.
• EXP

Returns Euler's number, e (~2.718) raised to a power.

EXP(2)
 exponent (number) The exponent to raise e to.
• FACT

The FACT function returns the factorial of a number.

FACT(3)
 value (number) The number or reference to a number whose factorial will be calculated and returned.
• FACTDOUBLE

Returns the "double factorial" of a number.

FACTDOUBLE(6)
 value (number) The number or reference to a number whose double factorial will be calculated and returned.
• FLOOR

The FLOOR function rounds a number down to the nearest integer multiple of specified significance.

FLOOR(23.25,0.1)
 value (number) The value to round down to the nearest integer multiple of factor. factor (number) Optional: The number to whose multiples value will be rounded. Factor may not be equal to 0.
• FLOOR_MATH

Rounds a number down, to the nearest integer or to the nearest multiple of significance

FLOOR_MATH(6.7)
 number (number) The number that should be rounded.
• FLOOR_PRECISE

Rounds a number the nearest integer or to the nearest multiple of significance. Regardless of the sign of the number, the number is rounded up.

FLOOR_PRECISE(6.7)
 number (number) The number that should be rounded.
• FMOD

Returns the floating point remainder (modulo) of the division of the arguments

FMOD(5.7, 1.3)
 x (number) The dividend y (number) The divisor
• GCD

Returns the greatest common divisor of one or more integers.

GCD(24,96)
 value1 (number) The first value or range whose factors to consider in a calculation to find the greatest common divisor. value2 (number) Optional: Additional values or ranges whose factors to consider to find the greatest common divisor.
• GT

Returns `TRUE` if the first argument is strictly greater than the second, and `FALSE` otherwise. Equivalent to the `>` operator.

GT(2,3)
 value1 (number) The value to test as being greater than value2. value2 (number) The second value.
• GTE

Returns `TRUE` if the first argument is greater than or equal to the second, and `FALSE` otherwise. Equivalent to the `>=` operator.

GTE(2,3)
 value1 (number) The value to test as being greater than or equal to value2. value2 (number) The second value.
• HYPOT

Calculate the length of the hypotenuse of a right-angle triangle

HYPOT(4,4)
 x (number) Length of first side y (number) Length of second side
• IF_NUMBER_EQUAL

Determines whether the first number is equal with second

IF_NUMBER_EQUAL(3,3)
 value1 (number) First number value2 (number) Second number
• IF_NUMBER_GREATER

Determines whether the first number is greater than second

IF_NUMBER_GREATER(4,3)
 value1 (number) First number value2 (number) Second number
• INT

Rounds a number down to the nearest integer that is less than or equal to it.

INT(99.44)
 value (number) The value to round down to the nearest integer.
• IS_FINITE

Finds whether a value is a legal finite number

IS_FINITE(1)
 val (number) The value to check
• IS_INFINITE

Finds whether a value is infinite

IS_INFINITE(1)
 val (number) The value to check
• IS_NAN

Finds whether a value is not a number

IS_NAN(ACOS(8))
 val (number) The value to check
• LCM

Returns the least common multiple of one or more integers.

LCM(2,3)
 value1 (number) The first value or range whose factors to consider in a calculation to find the least common multiple. value2 (number) Optional: Additional values or ranges whose factors to consider to find the least common multiple.
• LN

Returns the the logarithm of a number, base e (Euler's number).

LN(100)
 value (number) The value for which to calculate the logarithm, base e. Value must be positive.
• LOG

Returns the the logarithm of a number given a base.

LOG(128,2)
 value (number) The value for which to calculate the logarithm given base. Value must be positive. base (number) The base to use for calculation of the logarithm.
• LOG10

Returns the the logarithm of a number, base 10.

LOG10(100)
 value (number) The value for which to calculate the logarithm, base 10. value must be positive.
• LT

Returns `TRUE` if the first argument is strictly less than the second, and `FALSE` otherwise. Equivalent to the `<` operator.

LT(2,3)
 value1 (number) The value to test as being less than value2. value2 (number) The second value.
• LTE

Returns `TRUE` if the first argument is less than or equal to the second, and `FALSE` otherwise. Equivalent to the `<=` operator.

LTE(2,3)
 value1 (number) The value to test as being less than or equal to value2. value2 (number) The second value.
• MAKE_NEGATIVE

Transforms a number to a negative, even if it is negative

MAKE_NEGATIVE(123)
 number (number) The number to transform
• MAKE_POSITIVE

Transforms a number to a positive, even if it is positive

MAKE_POSITIVE(-123)
 number (number) The number to transform
• MDETERM

Returns the matrix determinant of a square matrix specified as an array or range.

MDETERM({var1})
 square_matrix (array) An array or range with an equal number of rows and columns representing a matrix whose determinant will be calculated.
• MINVERSE

Returns the multiplicative inverse of a square matrix specified as an array or range.

MINVERSE({var1})
 square_matrix (array) An array or range with an equal number of rows and columns representing a matrix whose multiplicative inverse will be calculated.
• MMULT

Calculates the matrix product of two matrices specified as arrays or ranges.

MMULT({var1},{var2})
 matrix1 (array) The first matrix in the matrix multiplication operation, represented as an array or range. matrix2 (array) The second matrix in the matrix multiplication operation, represented as an array or range.
• MOD

Returns the result of the modulo operator, the remainder after a division operation.

MOD(10,4)
 dividend (number) The number to be divided to find the remainder. divisor (number) The number to divide by.
• MROUND

Rounds one number to the nearest integer multiple of another.

MROUND(21,14)
 value (number) The number to round to the nearest integer multiple of another. factor (number) The number to whose multiples value will be rounded.
• MT_RAND

Generate a random value via the Mersenne Twister Random Number Generator

MT_RAND(5,15)
 min (number) Optional lowest value to be returned (default: 0) max (number) Optional highest value to be returned
• MULTINOMIAL

Returns the factorial of the sum of values divided by the product of the values' factorials.

MULTINOMIAL(1,2,3)
 value1 (number) The first value or range to consider. value2 (number) Additional values or ranges to consider.
• MULTIPLY

Multiply numbers

MULTIPLY(2,3)
 value1 (number) Multiplicands value2 (number) Multiplier
• ODD

Rounds a number up to the nearest odd integer.

ODD(2)
 value (number) The value to round to the next greatest odd number.
• PI

The PI function returns the value of pi to 9 decimal places.

PI()
• POW

Exponential expression

POW(2,8)
 base (number) The base to use exp (number) The exponent
• POWER

Returns a number raised to a power.

POWER(4,0.5)
 base (number) The number to raise to the exponent power. If base is negative, exponent must be an integer. exponent (number) The exponent to raise base to.
• PRODUCT

Returns the result of multiplying a series of numbers together.

PRODUCT(1,2,3,4,5)
 factor1 (number) The first number or range to calculate for the product. factor2 (number) Additional values to multiply by.
• QUOTIENT

Returns one number divided by another, without the remainder.

QUOTIENT(4,2)
 dividend (number) The number to be divided. divisor (number) The number to divide by (cannot equal 0).

Converts the radian number to the equivalent number in degrees

 angle (number) The angle to convert from degrees to radians.
• RAND

Returns a random number between 0 inclusive and 1 exclusive.

RAND()
• RANDBETWEEN

Returns a uniformly random integer between two values, inclusive.

RANDBETWEEN(1,10)
 low (number) The low end of the random range. high (number) The high end of the random range.
• ROMAN

Formats a number in Roman numerals.

ROMAN(499,0)
 number (number) The number to format, between 1 and 3999, inclusive. rule_relaxation (number) Optional: 0 by default. The degree to which traditional syntax rules may be relaxed, between 0 and 4 inclusive.
• ROUND

The ROUND function rounds a number to a certain number of decimal places according to standard rules.

ROUND(99.44,1)
 value (number) The value to round to places number of places. places (number) Optional: The number of decimal places to which to round.
• ROUNDDOWN

The ROUNDDOWN function rounds a number to a certain number of decimal places, always rounding down to the next valid increment.

ROUNDDOWN(99.44,1)
 value (number) The value to round to places number of places, always rounding down. places (number) Optional: The number of decimal places to which to round.
• ROUNDUP

Rounds a number to a certain number of decimal places, always rounding up to the next valid increment.

ROUNDUP(99.44,1)
 value (number) The value to round to places number of places, always rounding up. places (number) Optional: The number of decimal places to which to round.
• SEC

The SEC function returns the secant of an angle measured in radians.

SEC(3.14)
 angle (number) The angle to find the secant of, measured in radians.
• SECH

The SECH function returns the hyperbolic secant of an angle.

SECH(1)
 value (number) Any real value to calculate the hyperbolic secant of.
• SEQUENCE

Generates a list of sequential numbers in an array, such as 1, 2, 3, 4

SEQUENCE(10,5,0,3)
 rows (number) Number of rows to return. columns (number) Optional: Number of columns to return.
• SERIESSUM

Given parameters x, n, m, and a, returns the power series sum a1xn + a2x(n+m) + ... + aix(n+(i-1)m), where i is the number of entries in range `a`.

SERIESSUM(1,0,2,{var2})
 x (number) The input to the power series. Varies depending on the type of approximation, may be angle, exponent, or some other value. n (number) The initial power to which to raise x in the power series.
• SIGN

Given an input number, returns `-1` if it is negative, `1` if positive, and `0` if it is zero.

SIGN(-42)
 value (number) The value whose sign will be evaluated.
• SIN

The SIN function returns the sine of an angle provided in radians.

SIN(1)
 angle (number) The angle to find the sine of, in radians.
• SINH

The SINH function returns the hyperbolic sine of any real number.

SINH(1)
 value (number) Any real value to calculate the hyperbolic sine of.
• SQRT

Returns the positive square root of a positive number.

SQRT(9)
 value (number) The number for which to calculate the positive square root.
• SQRTPI

Returns the positive square root of the product of Pi and the given positive number.

SQRTPI(9)
 value (number) The number which will be multiplied by Pi and have the product's square root returned
• SUBSTRACT

Substract numbers

SUBSTRACT(10,2)
 value1 (number) Minuend value2 (number) Subtrahend
• SUBTOTAL

Returns a subtotal for a vertical range of variables using a specified aggregation function.

SUBTOTAL(1,{var1},{var2})
 function_code (number) The function to use in subtotal aggregation. 1 - AVERAGE, 2 - COUNT, 3 - COUNTA, 4 - MAX, 5 - MIN, 6 - PRODUCT, 7 - STDEV, 8 - STDEVP, 9 - SUM, 10 - VAR, 11 - VARP range1 (array) The first range over which to calculate a subtotal.
• SUM

Returns the sum of a series of numbers and/or variables.

SUM(1,2,3,4,5)
 value1 (mixed) The first number or range to add together. value2 (mixed) Optional - Additional numbers or ranges to add to value1.
• SUMIF

Returns a conditional sum across a range.

SUMIF({var1},">20")
 range (array) The range which is tested against criterion. criterion (string) The pattern or test to apply to range.
• SUMPRODUCT

The SUMPRODUCT function calculates the sum of the products of corresponding entries in 2 equally sized arrays or ranges.

SUMPRODUCT({var1},{var2})
 array1 (array) The first array or range whose entries will be multiplied with corresponding entries in the second such array or range. array2 (array) Optional - {1,1,1,...} with same length as array1 by default ] - The second array or range whose entries will be multiplied with corresponding entries in the first such array or range.
• SUMSQ

Returns the sum of the squares of a series of numbers and/or variables.

SUMSQ(1,2,3,4,5)
 value1 (number) The first number or range whose squares to add together. value2 (number) Optional: Additional numbers or ranges whose squares to add to the square(s) of value1.
• SUMX2MY2

Calculates the sum of the differences of the squares of values in two arrays.

SUMX2MY2([1,2,3],[4,5,6])
 array_x (array) The array or range of values whose squares will be reduced by the squares of corresponding entries in array_y and added together. array_y (array) The array or range of values whose squares will be subtracted from the squares of corresponding entries in array_x and added together.
• SUMX2PY2

Calculates the sum of the sums of the squares of values in two arrays.

SUMX2PY2([1,2,3],[4,5,6])
 array_x (array) The array or range of values whose squares will be added to the squares of corresponding entries in array_y and added together. array_y (array) The array or range of values whose squares will be added to the squares of corresponding entries in array_x and added together.
• SUMXMY2

Calculates the sum of the squares of differences of values in two arrays.

SUMXMY2([1,2,3],[4,5,6])
 array_x (array) The array or range of values that will be reduced by corresponding entries in array_y, squared, and added together. array_y (array) The array or range of values that will be subtracted from corresponding entries in array_x, the result squared, and all such results added together.
• TAN

The TAN function returns the tangent of an angle provided in radians.

TAN(1)
 angle (number) The angle to find the tangent of, in radians.
• TANH

The TANH function returns the hyperbolic tangent of any real number.

TANH(1)
 value (number) Any real value to calculate the hyperbolic tangent of.
• TRUNC

Truncates a number to a certain number of significant digits by omitting less significant digits.

TRUNC(3.141592654,2)
 value (number) The value to be truncated. places (number) Optional: The number of significant digits to the right of the decimal point to retain.