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GAMMALN Function

Excel 2007+, Excel 2010+, Excel 2013+, Excel 2016+, Excel 2019+, Excel 365

Summary

The GAMMALN function computes the natural logarithm of the gamma function, Γ(x), providing essential functionality for statistical calculations, probability distributions, and advanced mathematical analysis in Excel.

Syntax

GAMMALN(x)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	The value at which to evaluate the gamma function's natural logarithm. Must be greater than zero.

Using the GAMMALN Function

GAMMALN serves as a foundational mathematical function for advanced Excel analysis, particularly in statistics and engineering. It efficiently computes the logarithm of the gamma function, which extends the factorial concept to real numbers and forms the basis for many probability density functions.

Common GAMMALN Examples

Basic GAMMALN Calculation

=GAMMALN(4)

Returns approximately 1.7917595, which is ln(Γ(4)) = ln(6) since Γ(4) = 3! = 6.

Factorial Approximation

=EXP(GAMMALN(6))

Approximates 5! = 120. Returns approximately 120 since EXP(GAMMALN(n+1)) ≈ n!.

Statistical Application

=GAMMALN(B2)

Calculates ln(Γ(x)) where B2 contains shape parameter values for gamma distribution analysis.

Frequently Asked Questions

GAMMALN(4) = ln(Γ(4)) = ln(3!) = ln(6) ≈ 1.7917595.

GAMMALN prevents numeric overflow for large values and works with non-integer inputs unlike FACT function.

Yes, GAMMALN works with any positive real number, making it more versatile than integer-only factorial functions.

Common Errors and Solutions

#NUM! error

Cause: Input value x ≤ 0

Solution: Ensure x > 0. Gamma function is undefined for non-positive numbers.

#VALUE! error

Cause: Non-numeric input

Solution: Verify x contains a valid positive number, not text or blank cells.

Notes

For integer n, EXP(GAMMALN(n+1)) produces the same result as FACT(n)
GAMMALN is more numerically stable than computing ln(FACT(x)) directly
Use GAMMALN.PRECISE for higher precision in Excel 2010+
Essential for gamma, chi-squared, and exponential distribution calculations

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+, Excel 2010+, Excel 2013+, Excel 2016+, Excel 2019+, Excel 365