GAMMA.DIST in Google Sheets: Shape, Scale and Probability
Use GAMMA.DIST in Google Sheets for cumulative probabilities or densities, with shape and scale parameters, interval examples and documented zero-input restrictions.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =GAMMA.DIST(6,2,3,TRUE) has expected result 0.5939941503. It is the cumulative probability at 6 for a gamma distribution with shape 2 and scale 3. FALSE requests density instead.
Syntax and exact parameter roles
=GAMMA.DIST(x, alpha, beta, cumulative)
The Google GAMMA.DIST reference identifies alpha as shape and beta as scale. Both must be positive numerical values. They are not interchangeable.
x: numerical point at which to evaluate the model.alpha: shape parameter.beta: scale parameter, in the same units as x.cumulative: TRUE for the left-tail cumulative probability; FALSE for density.
The page does not establish an omitted-flag default. Use all four arguments. It also gives a specific x restriction: when alpha is at most 1 and cumulative is FALSE, x must be strictly positive; otherwise x may be zero or positive. Preserve this condition when building input validation.
Worked example: a synthetic service-duration model
Assume durations in minutes follow a chosen gamma model with shape 2 and scale 3. Enter 3, 6 and 9 in A2:A4. Put 2 in D1 and 3 in E1.
In B2, enter and fill down:
=GAMMA.DIST(A2,$D$1,$E$1,TRUE)
In C2, enter and fill down:
=GAMMA.DIST(A2,$D$1,$E$1,FALSE)
| Minutes | Expected cumulative probability | Expected density per minute |
|---|---|---|
| 3 | 0.2642411177 | 0.1226264804 |
| 6 | 0.5939941503 | 0.0902235222 |
| 9 | 0.8008517265 | 0.0497870684 |
The model assigns about 59.40% probability to durations at or below 6 minutes. A density of 0.0902235222 at that point is not a 9.02% probability of exactly 6 minutes. For a continuous model, an interval’s area supplies its probability.
These are synthetic parameters, not a fit to the three times in column A. Column A contains evaluation points, not observations from which the function estimates a model.
Check the shape-2 example independently
For this particular model, the CDF simplifies to:
=1-EXP(-A2/3)*(1+A2/3)
Its density simplifies to:
=A2*EXP(-A2/3)/9
Filling these formulas down reproduces the two result columns. They follow from NIST’s gamma density with zero location, shape 2 and scale 3. Changing shape requires a different expression; the shortcuts are not generic gamma formulas.
Advanced application: duration bands and a tail
The probability of a modeled duration between 3 and 9 minutes is:
=GAMMA.DIST(9,2,3,TRUE)-GAMMA.DIST(3,2,3,TRUE)
Expected result: 0.5366106089, about 53.66%. The probability above 9 minutes is:
=1-GAMMA.DIST(9,2,3,TRUE)
Expected result: 0.1991482735, about 19.91%.
A far-tail complement can lose relative precision when the CDF rounds extremely close to 1. Do not treat a displayed zero as proof that the modeled event is impossible. Keep full precision for calculations and round only for presentation.
Scale is not rate
Some mathematical sources parameterize gamma models with a rate instead of a scale. In that notation, scale is the reciprocal of rate. A supplied rate of 0.25 per minute corresponds to scale 4 minutes, not scale 0.25.
For shape 1 and scale 4, =GAMMA.DIST(4,1,4,TRUE) has expected result 0.6321205588. The independent exponential-model check is =1-EXP(-4/4). This special case makes a useful unit check when transferring model parameters.
Errors, aliases and version scope
Google documents GAMMADIST as synonymous with GAMMA.DIST. That does not imply all spreadsheet products use identical domain checks or coercion. Validate positive shapes and scales, the conditional x restriction and the explicit TRUE/FALSE argument before diagnosing an unexpected result. A scale that is accidentally entered as a rate can produce plausible but wrong numbers without a syntax error.
The reviewed reference does not enumerate every native error token or treatment of text and blank cells. No such behavior is inferred here. Current Google Sheets documentation confirms availability; original introduction date and first or last functioning numbered releases remain unestablished.
NOT_TESTED_IN_GOOGLE_SHEETS. Google and NIST pages were inspected on October 17, 2026. Outputs were independently checked by closed-form equations, numerical integration and gamma-distribution calculations, not native spreadsheet execution.