Gamma distribution calculator
Choose a calculation and enter shape k, scale θ and an x value.
How to use this page
- Choose density, CDF, upper tail or quantile.
- Enter shape k and scale θ.
- Provide x or a probability and read the result.
What this page does not do: The gamma distribution only takes non-negative values. Results use the shape-scale parameterization; confusing scale with rate produces a different distribution.
Further reading
The gamma distribution models positive right-skewed quantities such as time to several events or sums of positive waiting times. Shape k controls form and θ controls scale.
The CDF uses the regularized incomplete gamma function. A quantile is found numerically as the x value with the requested cumulative probability.
Frequently asked questions
Is scale θ the same as rate?
No. In a common parameterization rate β is the reciprocal of scale: β = 1/θ.
Is a density value a probability?
No. Interval probability is area under the density, not the height f(x) itself.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).