The Excel GAMMA.INV function returns the inverse of the gamma cumulative distribution: given a probability, alpha, and beta, it returns the x value at which GAMMA.DIST reaches that probability.
Syntax
| Argument | Description | |
|---|---|---|
probability | Required | The cumulative probability (0–1) you want to invert. |
alpha | Required | The shape parameter (α > 0), the same one used in GAMMA.DIST. |
beta | Required | The scale parameter (β > 0). |
How to use it
GAMMA.INV answers the reverse question to GAMMA.DIST: “what value of x gives me this cumulative probability?” It is the quantile (percentile) function of the gamma distribution:
Because it is the exact inverse, =GAMMA.INV(GAMMA.DIST(10,9,2,TRUE), 9, 2) returns 10 back. Feeding a probability of 0.5 gives the distribution's median.
Probability range: the first argument must be between 0 and 1. A probability of exactly 0, exactly 1, or outside that range returns #NUM!.
GAMMA.INV (Excel 2010+) replaces the legacy GAMMAINV function; both return the same quantiles.
Try it: interactive demo
Pick a GAMMA.INV example to see the formula and its result.
Practice workbook
Frequently asked questions
What is GAMMA.INV used for?
How is it related to GAMMA.DIST?
GAMMA.DIST(x, a, b, TRUE) turns an x into a probability; GAMMA.INV(p, a, b) turns that probability back into x. Chaining them returns the original number.What does a probability of 0.5 return?
When does GAMMA.INV error out?
probability is outside the open interval (0,1), or when alpha or beta is not positive — all return #NUM!.Master functions like this in one day
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