GAMMA.DIST in Excel: Distinguish Gamma Shape, Scale and Density

=GAMMA.DIST(x, alpha, beta, cumulative)

All four arguments are required. x is nonnegative, alpha is positive shape and beta is positive scale. The scale interpretation follows Microsoft’s density equation, whose exponential term is EXP(−x/beta). TRUE selects cumulative probability; FALSE selects density.

Scale has the same units as x. A rate-based mathematical parameterization instead uses rate=1/beta. Entering a rate in the scale argument produces a different model unless they happen to be equal.

The mean is alphabeta and variance alphabeta^2. Those are mathematical summaries of the chosen gamma model, not parameter estimates or tests of whether observations follow that model.

Put 0, 2, 4, 6 and 8 in A2:A6. In B2 enter =GAMMA.DIST(A2,3,2,TRUE) and fill down. Independent cumulative targets are approximately 0, 0.0803013971, 0.3233235838, 0.5768099189 and 0.7618966944.

For integer shape three, set u=x/2. The cumulative expression is 1-EXP(-u)*(1+u+u^2/2). A second column evaluating that closed form supplies an independent audit for these particular parameters.

The model can describe a sum of three independent exponential waiting times, each with mean two, when those assumptions apply. Its mean is 6 and variance 12. Arbitrary sums of observed durations need not meet those assumptions.

At x=6, =GAMMA.DIST(6,3,2,FALSE) has independent density 0.1120209038. It is a curve height per unit of x, not the probability of exactly six in a continuous model.

For the interval from two through six, use =GAMMA.DIST(6,3,2,TRUE)-GAMMA.DIST(2,3,2,TRUE). The independent target is 0.4965085218.

The probability beyond eight is =1-GAMMA.DIST(8,3,2,TRUE), independently 0.2381033056. Use the appropriate cumulative difference or complement; subtracting densities does not produce a probability area.

When alpha=1, the gamma model is exponential. =GAMMA.DIST(3,1,2,TRUE) has independent target 0.7768698399, matching an exponential distribution with rate 0.5.

Doubling both x and beta leaves a gamma cumulative probability unchanged for fixed alpha. Thus the original GAMMA.DIST(6,3,2,TRUE) matches GAMMA.DIST(12,3,4,TRUE) mathematically. The density, however, halves when the horizontal scale doubles.

This is a useful unit-conversion check. Changing beta without changing x asks about a different distribution at the same measurement point.

Microsoft supplies x=10.00001131, alpha=9 and beta=2. The independent density is approximately 0.0326391304, and the cumulative probability approximately 0.0680940039, agreeing with the source’s rounded results.

Keep the supplied x precision when reproducing that example. It is close to ten but not literally ten. The separate GAMMA special function and GAMMA.INV distribution inverse are different operations; the shared name does not make them substitutes for the CDF.

Microsoft documents #VALUE! when x, alpha or beta is nonnumeric, and #NUM! for x<0, alpha≤0 or beta≤0. Use an explicit logical cumulative argument. Exact coercion of every other type was not native-tested.

At zero, density behavior depends on shape: the shape-three example has a mathematical density limit of zero, but shapes below one have a singular limit. Do not extrapolate one endpoint result to every gamma model or invent its native display.

Check rate-versus-scale confusion, a missing cumulative flag and incompatible units before interpreting an unexpected number. The official density image was freshly inspected; the worked results are independent calculations, not recorded Excel output or a guarantee of extreme-tail accuracy.

• 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.DIST 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.DIST 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.