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Statistics

Gamma Distribution Calculator

Evaluate a gamma cumulative probability using shape and scale parameters.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter shape, scale, value x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

CDF = 1−Q(shape,x/scale), using the regularized upper incomplete gamma Q.

A WORKED EXAMPLE

Using shape = 2, scale = 1, value x = 2, the result is 0.59399415. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Scale parameterization, not rate. Main result is P(X≤x); rate is the reciprocal of scale.

What to keep in mind

Scale parameterization, not rate. Main result is P(X≤x); rate is the reciprocal of scale. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this gamma distribution calculator?

Evaluate a gamma cumulative probability using shape and scale parameters. Enter shape, scale, value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Scale parameterization, not rate. Main result is P(X≤x); rate is the reciprocal of scale.

Methodology maintained by ClarityKit. How these tools are built and checked.