GAMMALN.PRECISE Function in Google Sheets: Formula, Examples & Troubleshooting

=GAMMALN.PRECISE(value)

The single argument is required. Google’s function catalog lists this exact spelling and directs readers to its GAMMALN reference, which defines a base-e logarithm and requires a positive input. There are no optional arguments in the documented signature.

That cross-reference supports the mathematical contract, not a claim that both spellings have identical numerical implementations. The word PRECISE is not evidence of a measured accuracy improvement.

For a positive integer n, the Gamma identity is Γ(n) = (n − 1)!. Therefore the log of n-factorial is obtained from GAMMALN.PRECISE(n + 1). The extra 1 matters. For positive noninteger input, Gamma continues the factorial-related function between integer points; it is not ordinary factorial rounding.

Create A1 n, B1 Gamma argument, and C1 ln(n!). Enter 0, 1, 3, 5, and 100 in A2:A6.

1. Enter =A2+1 in B2 and fill down through B6.
2. Enter =GAMMALN.PRECISE(B2) in C2 and fill down through C6.
3. Display about ten decimal places where useful.
4. Compare with the independently checked values:

For n = 3, 3! = 6, so the result is ln(6). For n = 5, 5! = 120. Both n = 0 and n = 1 give a factorial of 1, whose natural logarithm is 0. The zero in the first data row never goes directly into GAMMALN.PRECISE; the formula supplies 1.

This distinction prevents a frequent off-by-one mistake: GAMMALN.PRECISE(5) represents ln(4!), not ln(5!). Document whether an input column contains n or the already-shifted Gamma argument.

For integer n and k with 0 ≤ k ≤ n, the binomial coefficient satisfies:

ln(C(n,k)) = ln(n!) − ln(k!) − ln((n−k)!)

Put 10 in E2 and 3 in F2. In G2, calculate:

=GAMMALN.PRECISE(E2+1)-GAMMALN.PRECISE(F2+1)-GAMMALN.PRECISE(E2-F2+1)

The expected log-result is approximately 4.7874917428. To recover the small count for this example, put =EXP(G2) in H2. The mathematical result is 120, because 10 × 9 × 8 / (3 × 2 × 1) = 120.

Keeping the calculation in log space can make multiplicative expressions easier to combine: products become sums and ratios become differences. For very large models, retain the log-result if that is what the downstream calculation needs. Exponentiating every intermediate value can undo that advantage.

Do not claim this construction produces exact integers for every input in floating-point arithmetic. If a final rounded count is required, choose and document an appropriate rounding rule after checking the underlying model. Also check n and k before evaluation: positive Gamma arguments alone do not establish that a pair represents a valid integer combination problem.

At input 0.5, the identity Γ(0.5) = √π gives:

=GAMMALN.PRECISE(0.5)

The expected result is approximately 0.5723649429. This demonstrates why GAMMALN.PRECISE should not be implemented conceptually by rounding the input and applying an integer factorial. The product reference’s positive-input requirement is broader than a positive-integer requirement.

• The input is zero or negative: It is outside the documented positive-input contract. Check the model and any missing +1 shift; do not silently replace it with a convenient positive value.
• The result looks smaller than a factorial: This function returns a logarithm. Γ(6) is 120, while ln(Γ(6)) is about 4.78749.
• The result was compared with LOG10: GAMMALN.PRECISE uses natural logarithms, base e. A base-10 comparison is a different calculation.
• A combination formula is off by a factor: Recheck all three +1 shifts and confirm whether the desired count permits repeated selections.
• An imported input is text: Validate the underlying value. The reviewed reference does not establish exact text-coercion rules or error tokens.

Google’s current catalog establishes documented support for this spelling on the review date. The original introduction and any retirement or last-working version were not established. No accuracy ranking, unsupported alias, or cross-software equivalence is asserted.

See LN for natural logarithms, EXP to reverse a natural log when appropriate, POWER for exponentiation, and ROUND for an explicit rounding step.

First-party references reviewed October 17, 2026: Google Sheets function catalog and GAMMALN. Factorial, half-integer Gamma, and combination examples were independently calculated.