Mathematical Functions
This category contains the Mathematical functions for Calc. To open the Function Wizard, choose Insert  Function.
AGGREGATE
This function returns an aggregate result of the calculations in the range. You can use different aggregate functions listed below. The Aggregate function enables you to omit hidden rows, errors, SUBTOTAL and other AGGREGATE function results in the calculation.
SUMIFS
Returns the sum of the values of cells in a range that meets multiple criteria in multiple ranges.
ABS
Returns the absolute value of a number.
Syntax
ABS(Number)
Number is the value whose absolute value is to be calculated. The absolute value of a number is its value without the +/ sign.
Example
=ABS(56) returns 56.
=ABS(12) returns 12.
=ABS(0) returns 0.
ACOS
Returns the inverse trigonometric cosine (arc cosine) of a number.
Syntax
ACOS(Number)
This function returns the inverse trigonometric cosine of Number, that is the angle (in radians) whose cosine is Number. The angle returned is in the range 0.0 to +PI.
To return the angle in degrees, use the DEGREES function.
Example
=ACOS(1) returns 3.14159265358979 (PI radians)
=DEGREES(ACOS(0.5)) returns 60. The cosine of 60 degrees is 0.5.
ACOSH
Returns the inverse hyperbolic cosine of a number.
Syntax
ACOSH(Number)
This function returns the inverse hyperbolic cosine of Number, that is the number whose hyperbolic cosine is Number.
Number must be greater than or equal to +1.0.
Example
=ACOSH(1) returns 0.
=ACOSH(COSH(4)) returns 4.
ACOT
Returns the inverse trigonometric cotangent (arc cotangent) of the given number.
Syntax
ACOT(Number)
This function returns the inverse trigonometric cotangent of Number, that is the angle (in radians) whose cotangent is Number. The angle returned is in the range 0.0 to +PI.
To return the angle in degrees, use the DEGREES function.
Example
=ACOT(1) returns 0.785398163397448 (PI/4 radians).
=DEGREES(ACOT(1)) returns 45. The tangent of 45 degrees is 1.
ACOTH
Returns the inverse hyperbolic cotangent of the given number.
Syntax
ACOTH(Number)
This function returns the inverse hyperbolic cotangent of Number, that is the number whose hyperbolic cotangent is Number.
An error results if Number is in the range 1.0 to +1.0 inclusive.
Example
=ACOTH(1.1) returns inverse hyperbolic cotangent of 1.1, approximately 1.52226.
ASIN
Returns the inverse trigonometric sine (arc sine) of a number.
Syntax
ASIN(Number)
This function returns the inverse trigonometric sine of Number, that is the angle (in radians) whose sine is Number. The angle returned is in the range PI/2 to +PI/2.
To return the angle in degrees, use the DEGREES function.
Example
=ASIN(0) returns 0.
=ASIN(1) returns 1.5707963267949 (PI/2 radians).
=DEGREES(ASIN(0.5)) returns 30. The sine of 30 degrees is 0.5.
ASINH
Returns the inverse hyperbolic sine of a number.
Syntax
ASINH(Number)
This function returns the inverse hyperbolic sine of Number, that is the number whose hyperbolic sine is Number.
Example
=ASINH(90) returns approximately 5.1929877.
=ASINH(SINH(4)) returns 4.
ATAN
Returns the inverse trigonometric tangent (arc tangent) of a number.
Syntax
ATAN(Number)
This function returns the inverse trigonometric tangent of Number, that is the angle (in radians) whose tangent is Number. The angle returned is in the range PI/2 to +PI/2.
To return the angle in degrees, use the DEGREES function.
Example
=ATAN(1) returns 0.785398163397448 (PI/4 radians).
=DEGREES(ATAN(1)) returns 45. The tangent of 45 degrees is 1.
ATAN2
Returns the inverse trigonometric tangent (arc tangent) of the specified x and ycoordinates.
Syntax
ATAN2(NumberX; NumberY)
NumberX is the value for the xcoordinate.
NumberY is the value for the ycoordinate.
ATAN2 returns the inverse trigonometric tangent, that is, the angle (in radians) between the xaxis and a line from point NumberX, NumberY to the origin. The angle returned is in the range PI to +PI.
To return the angle in degrees, use the DEGREES function.
Example
=ATAN2(20;20) returns 0.785398163397448 (PI/4 radians).
=DEGREES(ATAN2(12.3;12.3)) returns 45. The tangent of 45 degrees is 1.
ATANH
Returns the inverse hyperbolic tangent of a number.
Syntax
ATANH(Number)
This function returns the inverse hyperbolic tangent of Number, that is the number whose hyperbolic tangent is Number.
Number must obey the condition 1.0 < Number < +1.0.
Example
=ATANH(0) returns 0.
CEILING
Rounds a number up to the nearest multiple of Significance.
Syntax
CEILING(Number; Significance; Mode)
Number is the number that is to be rounded up.
Significance is the number that the value is to be rounded up to a multiple of.
Mode is an optional value. If the Mode value is given and not equal to zero, and if Number and Significance are negative, then rounding is done based on the absolute value of Number, i.e. negative numbers are rounded away from zero. If the Mode value is equal to zero or is not given, negative numbers are rounded towards zero.
If the spreadsheet is exported to Microsoft Excel, the CEILING function is exported as the equivalent CEILING.MATH function that exists since Excel 2013. If you plan to use the spreadsheet with earlier Excel versions, use either CEILING.PRECISE that exists since Excel 2010, or CEILING.XCL that is exported as the CEILING function compatible with all Excel versions. Note that CEILING.XCL always rounds away from zero.
Example
=CEILING(11;2) returns 10
=CEILING(11;2;0) returns 10
=CEILING(11;2;1) returns 12
CEILING.MATH
Rounds a number up to the nearest multiple of Significance.
Syntax
CEILING.MATH(Number; Significance; Mode)
Number is the number that is to be rounded up.
Significance is the number that the value is to be rounded up to a multiple of.
Mode is an optional value. If the Mode value is given and not equal to zero, and if Number and Significance are negative, then rounding is done based on the absolute value of Number, i.e. negative numbers are rounded away from zero. If the Mode value is equal to zero or is not given, negative numbers are rounded towards zero.
This function exists for interoperability with Microsoft Excel 2013 or newer.
Example
=CEILING.MATH(10;3) returns 9
=CEILING.MATH(10;3;0) returns 9
=CEILING.MATH(10;3;1) returns 12
CEILING.PRECISE
Rounds a number up to the nearest multiple of Significance, regardless of sign of Significance
Syntax
CEILING.PRECISE(Number; Significance)
Number (required) is the number that is to be rounded up.
Significance (optional) is the number that the value is to be rounded up to a multiple of.
Example
=CEILING.PRECISE(11;2) returns 10
CEILING.XCL
Rounds a number away from zero to the nearest multiple of Significance.
Syntax
CEILING.XCL(Number; Significance)
Number is the number that is to be rounded.
Significance is the value that the number is to be rounded to a multiple of.
This function exists for interoperability with Microsoft Excel 2007 or older versions.
Example
=CEILING.XCL(1;3) returns 3
=CEILING.XCL(7;4) returns 8
=CEILING.XCL(10;3) returns 12
COMBIN
Returns the number of combinations for a given number of objects (without repetition).
Syntax
COMBIN(Count1; Count2)
Count1 is the number of items in the set.
Count2 is the number of items to choose from the set.
COMBIN returns the number of ordered ways to choose these items. For example if there are 3 items A, B and C in a set, you can choose 2 items in 3 different ways, namely AB, AC and BC.
COMBIN implements the formula: Count1!/(Count2!*(Count1Count2)!)
Example
=COMBIN(3;2) returns 3.
COMBINA
Returns the number of combinations of a subset of items including repetitions.
Syntax
COMBINA(Count1; Count2)
Count1 is the number of items in the set.
Count2 is the number of items to choose from the set.
COMBINA returns the number of unique ways to choose these items, where the order of choosing is irrelevant, and repetition of items is allowed. For example if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AB, BA, AC, CA, BC and CB.
COMBINA implements the formula: (Count1+Count21)! / (Count2!(Count11)!)
Example
=COMBINA(3;2) returns 6.
CONVERT_OOO
Converts a value from one unit of measurement to another unit of measurement. The conversion factors are given in a list in the configuration.
At one time the list of conversion factors included the legacy European currencies and the euro (see examples below). We suggest using the new function EUROCONVERT for converting these currencies.
Syntax
CONVERT_OOO(value;"text";"text")
Example
=CONVERT_OOO(100;"ATS";"EUR") returns the Euro value of 100 Austrian Schillings.
=CONVERT_OOO(100;"EUR";"DEM") converts 100 Euros into German Marks.
COS
Returns the cosine of the given angle (in radians).
Syntax
COS(Number)
Returns the (trigonometric) cosine of Number, the angle in radians.
To return the cosine of an angle in degrees, use the RADIANS function.
Examples
=COS(PI()*2) returns 1, the cosine of 2*PI radians.
=COS(RADIANS(60)) returns 0.5, the cosine of 60 degrees.
COSH
Returns the hyperbolic cosine of a number.
Syntax
COSH(Number)
Returns the hyperbolic cosine of Number.
Example
=COSH(0) returns 1, the hyperbolic cosine of 0.
COT
Returns the cotangent of the given angle (in radians).
Syntax
COT(Number)
Returns the (trigonometric) cotangent of Number, the angle in radians.
To return the cotangent of an angle in degrees, use the RADIANS function.
The cotangent of an angle is equivalent to 1 divided by the tangent of that angle.
Examples:
=COT(PI()/4) returns 1, the cotangent of PI/4 radians.
=COT(RADIANS(45)) returns 1, the cotangent of 45 degrees.
COTH
Returns the hyperbolic cotangent of a given number (angle).
Syntax
COTH(Number)
Returns the hyperbolic cotangent of Number.
Example
=COTH(1) returns the hyperbolic cotangent of 1, approximately 1.3130.
CSC
Returns the cosecant of the given angle (in radians). The cosecant of an angle is equivalent to 1 divided by the sine of that angle
Syntax
CSC(Number)
Returns the (trigonometric) cosecant of Number, the angle in radians.
To return the cosecant of an angle in degrees, use the RADIANS function.
Examples
=CSC(PI()/4) returns approximately 1.4142135624, the inverse of the sine of PI/4 radians.
=CSC(RADIANS(30)) returns 2, the cosecant of 30 degrees.
CSCH
Returns the hyperbolic cosecant of a number.
Syntax
CSCH(Number)
Returns the hyperbolic cosecant of Number.
Example
=CSCH(1) returns approximately 0.8509181282, the hyperbolic cosecant of 1.
DEGREES
Converts radians into degrees.
Syntax
DEGREES(Number)
Number is the angle in radians to be converted to degrees.
Example
=DEGREES(PI()) returns 180 degrees.
EUROCONVERT
Converts between old European national currency and to and from euro.
Syntax
EUROCONVERT(Value; "From_currency"; "To_currency", full_precision, triangulation_precision)
Value is the amount in the currency to be converted.
From_currency and To_currency are the currency units to convert from and to respectively. These must be text, the official abbreviation for the currency (for example, "EUR"). The rates (shown per euro) were set by the European Commission.
Full_precision is optional. If omitted or False, the result is rounded according to the decimals of the To currency. If Full_precision is True, the result is not rounded.
Triangulation_precision is optional. If Triangulation_precision is given and >=3, the intermediate result of a triangular conversion (currency1,EUR,currency2) is rounded to that precision. If Triangulation_precision is omitted, the intermediate result is not rounded. Also if To currency is "EUR", Triangulation_precision is used as if triangulation was needed and conversion from EUR to EUR was applied.
Examples
=EUROCONVERT(100;"ATS";"EUR") converts 100 Austrian Schillings into euro.
=EUROCONVERT(100;"EUR";"DEM") converts 100 euro into German Marks.
EVEN
Rounds a positive number up to the next even integer and a negative number down to the next even integer.
Syntax
EVEN(Number)
Returns Number rounded to the next even integer up, away from zero.
Examples
=EVEN(2.3) returns 4.
=EVEN(2) returns 2.
=EVEN(0) returns 0.
=EVEN(0.5) returns 2.
EXP
Returns e raised to the power of a number. The constant e has a value of approximately 2.71828182845904.
Syntax
EXP(Number)
Number is the power to which e is to be raised.
Example
=EXP(1) returns 2.71828182845904, the mathematical constant e to Calc's accuracy.
FACT
Returns the factorial of a number.
Syntax
FACT(Number)
Returns Number!, the factorial of Number, calculated as 1 * 2 * 3 * 4 * ... * Number.
=FACT(0) returns 1 by definition.
The factorial of a negative number returns the "invalid argument" error.
Example
=FACT(3) returns 6.
=FACT(0) returns 1 (by definition).
FLOOR
Rounds a number down to the nearest multiple of Significance.
Syntax
FLOOR(Number; Significance; Mode)
Number is the number that is to be rounded down.
Significance is the value that the number is to be rounded down to a multiple of.
Mode is an optional value. If the Mode value is given and not equal to zero, and if Number and Significance are negative, then rounding is done based on the absolute value of Number, i.e. negative numbers are rounded towards zero. If the Mode value is equal to zero or is not given, negative numbers are rounded away from zero.
If the spreadsheet is exported to Microsoft Excel, the FLOOR function is exported as the equivalent FLOOR.MATH function that exists since Excel 2013. If you plan to use the spreadsheet with earlier Excel versions, use either FLOOR.PRECISE that exists since Excel 2010, or FLOOR.XCL that is exported as the FLOOR function compatible with all Excel versions. Note that FLOOR.XCL always rounds towards zero.
Example
=FLOOR( 11;2) returns 12
=FLOOR( 11;2;0) returns 12
=FLOOR( 11;2;1) returns 10
FLOOR.PRECISE
Rounds a number down to the nearest multiple of Significance, regardless of sign of Significance
Syntax
FLOOR.PRECISE(Number; Significance)
Number is the number that is to be rounded down.
Significance is the value that the number is to be rounded down to a multiple of.
Example
=FLOOR.PRECISE( 11;2) returns 12
GCD
Returns the greatest common divisor of two or more integers.
The greatest common divisor is the positive largest integer which will divide, without remainder, each of the given integers.
Syntax
GCD(Integer1; Integer2; ... Integer30)
Integer1; Integer2; ... Integer30 are 1 to 30 integers for which the greatest common divisor is to be calculated.
Example
=GCD(16;32;24) gives the result 8, because 8 is the largest number that can divide 16, 24 and 32 without a remainder.
=GCD(B1:B3) where cells B1, B2, B3 contain 9, 12, 9 gives 3.
GCD_EXCEL2003
The result is the greatest common divisor of a list of numbers.
Syntax
GCD_EXCEL2003(Number(s))
Number(s) is a list of 1 to 30 numbers.
Example
=GCD_EXCEL2003(5;15;25) returns 5.
INT
Rounds a number down to the nearest integer.
Syntax
INT(Number)
Returns Number rounded down to the nearest integer.
Negative numbers round down to the integer below.
Example
=INT(5.7) returns 5.
=INT(1.3) returns 2.
ISO.CEILING
Rounds a number up to the nearest multiple of Significance, regardless of sign of Significance
Syntax
ISO.CEILING(Number; Significance)
Number (required) is the number that is to be rounded up.
Significance (optional) is the number that the value is to be rounded up to a multiple of.
Example
=ISO.CEILING(11;2) returns 10
LCM
Returns the least common multiple of one or more integers.
Syntax
LCM(Integer1; Integer2; ... Integer30)
Integer1; Integer2; ... Integer30 are 1 to 30 integers for which the lowest common multiple is to be calculated.
Example
If you enter the numbers 512, 1024 and 2000 in the Integer 1, 2 and 3 text boxes, 128000 will be returned as the result.
LCM_EXCEL2003
The result is the lowest common multiple of a list of numbers.
Syntax
LCM_EXCEL2003(Number(s))
Number(s) is a list of 1 to 30 numbers.
Example
=LCM_EXCEL2003(5;15;25) returns 75.
LN
Returns the natural logarithm based on the constant e of a number. The constant e has a value of approximately 2.71828182845904.
Syntax
LN(Number)
Number is the value for which the natural logarithm is to be calculated.
Example
=LN(3) returns the natural logarithm of 3 (approximately 1.0986).
=LN(EXP(321)) returns 321.
LOG
Returns the logarithm of a number to the specified base.
Syntax
LOG(Number; Base)
Number is the value for which the logarithm is to be calculated.
Base (optional) is the base for the logarithm calculation. If omitted, Base 10 is assumed.
Example
=LOG(10;3) returns the logarithm to base 3 of 10 (approximately 2.0959).
=LOG(7^4;7) returns 4.
LOG10
Returns the base10 logarithm of a number.
Syntax
LOG10(Number)
Returns the logarithm to base 10 of Number.
Example
=LOG10(5) returns the base10 logarithm of 5 (approximately 0.69897).
MOD
Returns the remainder after a number is divided by a divisor.
Syntax
MOD(Dividend; Divisor)
For integer arguments this function returns Dividend modulo Divisor, that is the remainder when Dividend is divided by Divisor.
This function is implemented as Dividend  Divisor * INT(Dividend/Divisor) and this formula gives the result if the arguments are not integer.
Example
=MOD(22;3) returns 1, the remainder when 22 is divided by 3.
=MOD(11.25;2.5) returns 1.25.
MROUND
Returns a number rounded to the nearest multiple of another number.
Syntax
MROUND(Number; Multiple)
Returns Number rounded to the nearest multiple of Multiple.
An alternative implementation would be Multiple * ROUND(Number/Multiple).
Example
=MROUND(15.5;3) returns 15, as 15.5 is closer to 15 (= 3*5) than to 18 (= 3*6).
=MROUND(1.4;0.5) returns 1.5 (= 0.5*3).
MULTINOMIAL
Returns the factorial of the sum of the arguments divided by the product of the factorials of the arguments.
Syntax
MULTINOMIAL(Number(s))
Number(s) is a list of 1 to 30 numbers.
Example
=MULTINOMIAL(F11:H11) returns 1260, if F11 to H11 contain the values 2, 3 and 4. This corresponds to the formula =(2+3+4)! / (2!*3!*4!)
ODD
Rounds a positive number up to the nearest odd integer and a negative number down to the nearest odd integer.
Syntax
ODD(Number)
Returns Number rounded to the next odd integer up, away from zero.
Example
=ODD(1.2) returns 3.
=ODD(1) returns 1.
=ODD(0) returns 1.
=ODD(3.1) returns 5.
PI
Returns 3.14159265358979..., the value of the mathematical constant PI to 14 decimal places.
Syntax
PI()
Example
=PI() returns 3.14159265358979... as a rounded value.
POWER
Returns the result of a number raised to a power.
Syntax
POWER(Base; Power) or Base ^ Power
Returns Base raised to the power of Power.
The same result may be achieved by using the exponentiation operator ^:
Base^Power
Example
=POWER(4;3) returns 64, which is 4 to the power of 3.
=4^3 also returns 4 to the power of 3.
PRODUCT
Multiplies all the numbers given as arguments and returns the product.
Syntax
PRODUCT(Number1; Number2; ... Number30)
Number1; Number2; ... Number30 are 1 to 30 arguments whose product is to be calculated.
PRODUCT returns Number1 * Number2 * Number_3 * ... Number_N
Example
=PRODUCT(2;3;4) returns 24.
QUOTIENT
Returns the integer result of a division operation.
Syntax
QUOTIENT(Numerator; Denominator)
Returns the integer part of Numerator divided by Denominator.
QUOTIENT is equivalent to INT(numerator/denominator) for samesign numerator and denominator, except that it may report errors with different error codes. More generally, it is equivalent to INT(numerator/denominator/SIGN(numerator/denominator))*SIGN(numerator/denominator).
Example
=QUOTIENT(11;3) returns 3. The remainder of 2 is omitted.
RADIANS
Converts degrees to radians.
Syntax
RADIANS(Number)
Number is the angle in degrees to be converted to radians.
Example
=RADIANS(90) returns 1.5707963267949, which is PI/2 to Calc's accuracy.
RAND
Returns a random number in the range 0.0 to 1.0.
Syntax
RAND()
This function produces a new random number each time Calc recalculates. To force Calc to recalculate manually press F9.
To generate random numbers which never recalculate, copy cells each containing =RAND() and use
(with and not marked and marked).Example
=RAND() returns a random number in the range 0.0 to 1.0.
RANDBETWEEN
Returns an integer random number in a specified range.
Syntax
RANDBETWEEN(Bottom; Top)
Returns an integer random number between integers Bottom and Top (both inclusive).
This function produces a new random number each time that Calc recalculates. To force Calc to recalculate manually press Shift+CommandCtrl+F9.
To generate random numbers which never recalculate, copy cells containing this function and use
(with and not marked and marked).Example
=RANDBETWEEN(20;30) returns an integer in the range 20 to 30.
ROUND
Returns a number rounded to a certain number of decimal places.
Syntax
ROUND(Number; Count)
Returns Number rounded to Count decimal places. If Count is omitted or zero, the function rounds to the nearest integer. If Count is negative, the function rounds to the nearest 10, 100, 1000, etc.
This function rounds to the nearest number. See ROUNDDOWN and ROUNDUP for alternatives.
Example
=ROUND(2.348;2) returns 2.35
=ROUND(32.4834;3) returns 32.483. Change the cell format to see all decimals.
=ROUND(2.348;0) returns 2.
=ROUND(2.5) returns 3.
=ROUND(987.65;2) returns 1000.
ROUNDDOWN
Rounds a number down, towards zero, to a certain precision.
Syntax
ROUNDDOWN(Number; Count)
Returns Number rounded down (towards zero) to Count decimal places. If Count is omitted or zero, the function rounds down to an integer. If Count is negative, the function rounds down to the next 10, 100, 1000, etc.
This function rounds towards zero. See ROUNDUP and ROUND for alternatives.
Example
=ROUNDDOWN(1.234;2) returns 1.23.
=ROUNDDOWN(45.67;0) returns 45.
=ROUNDDOWN(45.67) returns 45.
=ROUNDDOWN(987.65;2) returns 900.
ROUNDUP
Rounds a number up, away from zero, to a certain precision.
Syntax
ROUNDUP(Number; Count)
Returns Number rounded up (away from zero) to Count decimal places. If Count is omitted or zero, the function rounds up to an integer. If Count is negative, the function rounds up to the next 10, 100, 1000, etc.
This function rounds away from zero. See ROUNDDOWN and ROUND for alternatives.
Example
=ROUNDUP(1.1111;2) returns 1.12.
=ROUNDUP(1.2345;1) returns 1.3.
=ROUNDUP(45.67;0) returns 46.
=ROUNDUP(45.67) returns 46.
=ROUNDUP(987.65;2) returns 1000.
SEC
Returns the secant of the given angle (in radians). The secant of an angle is equivalent to 1 divided by the cosine of that angle
Syntax
SEC(Number)
Returns the (trigonometric) secant of Number, the angle in radians.
To return the secant of an angle in degrees, use the RADIANS function.
Examples
=SEC(PI()/4) returns approximately 1.4142135624, the inverse of the cosine of PI/4 radians.
=SEC(RADIANS(60)) returns 2, the secant of 60 degrees.
SECH
Returns the hyperbolic secant of a number.
Syntax
SECH(Number)
Returns the hyperbolic secant of Number.
Example
=SECH(0) returns 1, the hyperbolic secant of 0.
SERIESSUM
Sums the first terms of a power series.
SERIESSUM(x;n;m;coefficients) = coefficient_1*x^n + coefficient_2*x^(n+m) + coefficient_3*x^(n+2m) +...+ coefficient_i*x^(n+(i1)m)
Syntax
SERIESSUM(X; N; M; Coefficients)
X is the input value for the power series.
N is the initial power
M is the increment by which to increase N
Coefficients is a series of coefficients. For each coefficient the series sum is extended by one section.
SIGN
Returns the sign of a number. Returns +1 if the number is positive, 1 if negative and 0 if zero.
Syntax
SIGN(Number)
Number is the number of which the sign is to be determined.
Example
=SIGN(3.4) returns 1.
=SIGN(4.5) returns 1.
SIN
Returns the sine of the given angle (in radians).
Syntax
SIN(Number)
Returns the (trigonometric) sine of Number, the angle in radians.
To return the sine of an angle in degrees, use the RADIANS function.
Example
=SIN(PI()/2) returns 1, the sine of PI/2 radians.
=SIN(RADIANS(30)) returns 0.5, the sine of 30 degrees.
SINH
Returns the hyperbolic sine of a number.
Syntax
SINH(Number)
Returns the hyperbolic sine of Number.
Example
=SINH(0) returns 0, the hyperbolic sine of 0.
SQRT
Returns the positive square root of a number.
Syntax
SQRT(Number)
Returns the positive square root of Number.
Number must be positive.
Example
=SQRT(16) returns 4.
=SQRT(16) returns an invalid argument error.
SQRTPI
Returns the square root of (PI times a number).
Syntax
SQRTPI(Number)
Returns the positive square root of (PI multiplied by Number).
This is equivalent to SQRT(PI()*Number).
Example
=SQRTPI(2) returns the square root of (2PI), approximately 2.506628.
SUBTOTAL
Calculates subtotals. If a range already contains subtotals, these are not used for further calculations. Use this function with the AutoFilters to take only the filtered records into account.
Syntax
SUBTOTAL(Function; Range)
Function is a number that stands for one of the following functions:
Function index (includes hidden values) 
Function index (ignores hidden values) 
Function 
1 
101 
AVERAGE 
2 
102 
COUNT 
3 
103 
COUNTA 
4 
104 
MAX 
5 
105 
MIN 
6 
106 
PRODUCT 
7 
107 
STDEV 
8 
108 
STDEVP 
9 
109 
SUM 
10 
110 
VAR 
11 
111 
VARP 
Use numbers 111 to include manually hidden rows or 101111 to exclude them; filteredout cells are always excluded.
Range is the range of cells included.
Example
You have a table in the cell range A1:B6 containing a bill of material for 10 students. Row 2 (Pen) is manually hidden. You want to see the sum of the figures that are displayed; that is, just the subtotal for the filtered rows. In this case the correct formula would be:
A 
B 

1 
ITEM 
QUANTITY 
2 
Pen 
10 
3 
Pencil 
10 
4 
Notebook 
10 
5 
Rubber 
10 
6 
Sharpener 
10 
=SUBTOTAL(9;B2:B6) returns 50.
=SUBTOTAL(109;B2:B6) returns 40.
SUM
Adds all the numbers in a range of cells.
Syntax
SUM(Number1; Number2; ...)
Number1; Number2; ... are 1 to 30 arguments whose sum is to be calculated.
Example
If you enter the numbers 2, 3 and 4 in the Number 1, 2 and 3 text boxes, 9 will be returned as the result.
=SUM(A1;A3;B5) calculates the sum of the three cells. =SUM(A1:E10) calculates the sum of all cells in the A1 to E10 cell range.
Conditions linked by AND can be used with the function SUM() in the following manner:
Example assumption: You have entered invoices into a table. Column A contains the date value of the invoice, column B the amounts. You want to find a formula that you can use to return the total of all amounts for only a specific month, e.g. only the amount for the period >=20080101 to <20080201. The range with the date values covers A1:A40, the range containing the amounts to be totalled is B1:B40. C1 contains the start date, 20080101, of the invoices to be included and C2 the date, 20080201, that is no longer included.
Enter the following formula as an array formula:
=SUM((A1:A40>=C1)*(A1:A40<C2)*B1:B40)
In order to enter this as an array formula, you must press the Shift+Command+ Ctrl+ Enter keys instead of simply pressing the Enter key to close the formula. The formula will then be shown in the Formula bar enclosed in braces.
{=SUM((A1:A40>=C1)*(A1:A40<C2)*B1:B40)}
The formula is based on the fact that the result of a comparison is 1 if the criterion is met and 0 if it is not met. The individual comparison results will be treated as an array and used in matrix multiplication, and at the end the individual values will be totalled to give the result matrix.
SUMIF
Adds the cells specified by a given criteria. This function is used to browse a range when you search for a certain value.
Syntax
SUMIF(Range; Criteria; SumRange)
Range is the range to which the criteria are to be applied.
Criteria is a reference to a cell containing the search criterion, or the search criterion itself. If the criterion is written into the formula, it must be enclosed with double quotes.
SumRange is the range from which values are summed. If this parameter has not been indicated, the values found in the Range are summed.
SUMIF supports the reference concatenation operator (~) only in the Criteria parameter and only if the optional SumRange parameter is not given.
Example
To sum only negative numbers: =SUMIF(A1:A10;"<0")
=SUMIF(A1:A10;">0";B1:10)  sums values from the range B1:B10 only if the corresponding values in the range A1:A10 are >0.
See COUNTIF() for some more syntax examples that can be used with SUMIF().
SUMSQ
If you want to calculate the sum of the squares of numbers (totalling up of the squares of the arguments), enter these into the text fields.
Syntax
SUMSQ(Number1; Number2; ... Number30)
Number1; Number2; ... Number30 are 1 to 30 arguments the sum of whose squares is to be calculated.
Example
If you enter the numbers 2, 3 and 4 in the Number 1, 2 and 3 text boxes, 29 is returned as the result.
TAN
Returns the tangent of the given angle (in radians).
Syntax
TAN(Number)
Returns the (trigonometric) tangent of Number, the angle in radians.
To return the tangent of an angle in degrees, use the RADIANS function.
Example
=TAN(PI()/4) returns 1, the tangent of PI/4 radians.
=TAN(RADIANS(45)) returns 1, the tangent of 45 degrees.
TANH
Returns the hyperbolic tangent of a number.
Syntax
TANH(Number)
Returns the hyperbolic tangent of Number.
Example
=TANH(0) returns 0, the hyperbolic tangent of 0.
TRUNC
Truncates a number by removing decimal places.
Syntax
TRUNC(Number; Count)
Returns Number with at most Count decimal places. Excess decimal places are simply removed, irrespective of sign.
TRUNC(Number; 0) behaves as INT(Number) for positive numbers, but effectively rounds towards zero for negative numbers.
The visible decimal places of the result correspond to the number of decimal places specified in LibreOffice  PreferencesTools  Options  LibreOffice Calc  Calculate.
Example
=TRUNC(1.239;2) returns 1.23. The 9 is omitted.
=TRUNC(1.234999;3) returns 1.234. All the 9s are omitted.