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#Statistical

GAMMA

Excel Functions

Extends factorial calculations to decimal numbers

Syntax

EXCEL
=GAMMA(number)

Arguments

Parameter Description
number A decimal number for which you want to calculate the gamma function value.

Return Value

Extended factorial for decimal numbers

Details

The GAMMA function returns the gamma function value Γ(n) for a given number. The key relationship to understand is that Γ(n) = (n - 1)!, which means Excel's GAMMA function essentially computes factorials shifted by one position. For example, GAMMA(5) returns 24, which is equivalent to 4! (4 factorial). Importantly, the gamma function extends this factorial concept to non-integer values, defining calculations like GAMMA(2.5) that would be undefined with traditional factorials. The GAMMA function is used for statistical calculations, probability distributions, and advanced mathematical modeling. The GAMMA function takes a single argument in this syntax: The argument number is the value for which you want to calculate the gamma function. Here are some basic examples showing both integer and n

Examples

Example #1 - Basic calculations

The GAMMA function takes a single argument in this syntax:

EXCEL
=GAMMA(number)
Example #1 - Basic calculations

The argument number is the value for which you want to calculate the gamma function. Here are some basic examples showing both integer and non-integer

EXCEL
=GAMMA(0.5) // returns 1.7724538509... (√π)
=GAMMA(2) // returns 1
=GAMMA(2.5) // returns 1.3293403881...
=GAMMA(5) // returns 24
Example #2 - Relationship to factorials

The example below demonstrates the relationship between the GAMMA function and factorials. For any positive integer n, GAMMA(n) equals (n-1)!.

EXCEL
=GAMMA(n) // returns (n-1)!
Example #3 - Error conditions

The GAMMA function returns #NUM! for zero and negative integers, and #VALUE! for non-numeric inputs.

EXCEL
=GAMMA(0) // returns #NUM! error
=GAMMA(-1) // returns #NUM! error
=GAMMA(-2) // returns #NUM! error
=GAMMA("text") // returns #VALUE! error

See Also

FACT GAMMALN GAMMA.DIST GAMMA.INV