GAMMA.INV in Excel: Find Gamma Percentiles and Verify the Forward Probability

=GAMMA.INV(probability, alpha, beta)

All three arguments are required. probability is the cumulative probability. alpha is positive shape, and beta is positive scale, with beta=1 defining the standard scale in Microsoft’s reference.

The inverse seeks x such that GAMMA.DIST(x,alpha,beta,TRUE)=probability. It does not invert GAMMA(x), the special function that generalizes factorials. A large gamma-function value is not therefore a valid probability input.

The output has the same measurement units as beta. The worked examples use strictly interior probabilities and positive parameters; native endpoint behavior is discussed separately below.

Put 0.25, 0.5 and 0.9 in A2:A4. Enter =GAMMA.INV(A2,3,2) in B2 and fill down. Independent targets are approximately 3.4545988357, 5.3481206274 and 10.6446406757.

The median is about 5.3481, while the mean is alpha*beta=6. A skewed gamma model need not have matching mean and median. Label a requested average separately from a requested percentile.

The 25th-to-90th-percentile interval contains 65% of this continuous model. Choosing arbitrary percentiles does not automatically create a central 95% interval or a confidence interval for a mean.

In C2 enter =GAMMA.DIST(B2,3,2,TRUE) and fill down. The mathematical targets are 0.25, 0.5 and 0.9.

For shape three and scale two, a second check is =1-EXP(-B2/2)*(1+B2/2+(B2/2)^2/2). This closed form should recover the same probability for the full stored quantile.

Retyping 5.35 instead of retaining the computed median changes the result. Small residuals can also reflect finite numerical precision. The independent checks use high precision but do not measure Excel’s own implementation tolerance.

At alpha=1 the model is exponential with scale beta. Its quantile is =-beta*LN(1-probability) for an interior probability.

=GAMMA.INV(0.8,1,2) independently targets 3.2188758249. Compare it with =-2*LN(1-0.8) as a direct mathematical check. A rate of 0.5 corresponds to scale two; using beta=0.5 instead would yield a different threshold.

For fixed shape and probability, doubling beta doubles the quantile. That property helps audit unit conversions, but changing shape is not a simple multiplication of every result.

Microsoft’s inverse example uses probability 0.068094, alpha 9 and beta 2, giving a displayed result 10.0000112. It is not exactly ten, and it need not reproduce another example’s x to every printed digit because the input probability is rounded.

If a spreadsheet computes the forward probability first, pass that cell directly into GAMMA.INV rather than using a shortened display value. The reference explicitly connects inverse precision to GAMMA.DIST precision.

A model quantile remains conditional on its parameters. This function does not estimate shape or scale, validate a waiting-time process, or attach a real-world guarantee to the threshold.

Microsoft documents #VALUE! for text arguments and #NUM! for probability<0, probability>1 or nonpositive alpha or beta. Its remarks do not explicitly exclude the probability-one endpoint, but an unbounded gamma model has no finite upper-end quantile. This guide makes no native result claim at zero or one; the executable examples stay inside the interval.

The reference says GAMMA.INV uses an iterative search and returns #N/A if it has not converged after 64 iterations. That is documented behavior, not a native trace observed in this review.

Check probability entry, rate-versus-scale interpretation and whether TRUE was used in the forward comparison. Avoid treating a mathematical round trip as a universal precision or convergence guarantee for extreme parameter values.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks GAMMA.INV as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft GAMMA.INV reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.