Summary

The Excel GAMMALN.PRECISE function returns the natural logarithm of the gamma function for a given number. It is the more accurate, modern replacement for the older GAMMALN function, and is recommended for new work. This function is useful for calculations involving large factorials or products, as working with logarithms helps avoid overflow and increases numerical stability.

Purpose 

To calculate the natural logarithm of the gamma function.

Return value 

A number representing the natural logarithm of the gamma function.

Syntax

=GAMMALN.PRECISE(x)
  • x - A positive real number for which you want to calculate the natural logarithm of the gamma function.

Using the GAMMALN.PRECISE function 

The GAMMALN.PRECISE function returns the natural logarithm of the gamma function, ln(Γ(n)), for a given number. This is useful in statistical calculations, such as those involving probability distributions, where the gamma function appears in the denominator and direct computation could result in very large or very small numbers.

For positive integers n, GAMMALN.PRECISE(n) is equivalent to LN((n-1)!). For example, the following formula calculates the natural logarithm of the gamma value for 5:

=GAMMALN.PRECISE(5) // returns 3.17805383

Key features

  • Returns the natural logarithm of the gamma function for decimal numbers
  • For positive integers n, GAMMALN.PRECISE(n) equals LN((n-1)!)
  • Accepts positive decimal numbers as input
  • Returns #NUM! error for zero and negative numbers
  • More accurate than the legacy GAMMALN function

Table of contents

Example #1 - Basic calculations

The GAMMALN.PRECISE function takes a single argument as input like this:

=GAMMALN.PRECISE(x)

The argument x is the value for which you want to calculate the natural logarithm of the gamma function. Here are some basic examples showing both integer and non-integer inputs:

=GAMMALN.PRECISE(0.5) // returns 0.57236494...
=GAMMALN.PRECISE(2.0) // returns 0
=GAMMALN.PRECISE(2.5) // returns 0.28468287...
=GAMMALN.PRECISE(4.0) // returns 1.79175947...

Excel GAMMALN.PRECISE function basic calculations example

Example #2 - Relationship to gamma and factorials

In general, the GAMMALN.PRECISE function is equivalent to the natural logarithm of the gamma function:

=GAMMALN.PRECISE(x) // returns LN(GAMMA(x))

This relationship makes the GAMMALN.PRECISE function useful for calculations involving large factorials, as it avoids direct computation of large numbers. For example, attempting to compute a large factorial directly with the GAMMA function can result in an error due to overflow:

=GAMMA(172) // returns #NUM! error

In contrast, using GAMMALN.PRECISE allows you to work with the logarithm of the gamma function, which avoids this problem and provides a valid result even for large inputs.

Excel table comparing GAMMA and GAMMALN.PRECISE for large x values, showing GAMMA returns huge numbers or #NUM! errors, while GAMMALN.PRECISE gives valid logarithmic results.

Example #3 - Error conditions

The GAMMALN.PRECISE function returns #NUM! for zero and negative numbers, and #VALUE! for non-numeric inputs.

=GAMMALN.PRECISE(0) // returns #NUM! error
=GAMMALN.PRECISE(-1) // returns #NUM! error
=GAMMALN.PRECISE(-2.5) // returns #NUM! error
=GAMMALN.PRECISE("text") // returns #VALUE! error

Excel GAMMALN.PRECISE function error examples

Formula definition

The GAMMALN.PRECISE function is defined as the natural logarithm of the gamma function. The function is mathematically equivalent to:

GAMMALN.PRECISE(x) = LN(GAMMA(x))

The function is plotted below, where Γ(x) is the gamma function.

Graph of the GAMMALN.PRECISE function, y = ln(Gamma(x)), showing a curve that decreases steeply for x near 0, reaches a minimum near x = 1, and then increases steadily for larger x, over the range x = 0 to x = 5.

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Dave Bruns

Hi - I'm Dave Bruns, and I run Exceljet with my wife, Lisa. Our goal is to help you work faster in Excel. We create short videos, and clear examples of formulas, functions, pivot tables, conditional formatting, and charts.