Gamma distribution calculator
Choose a calculation and enter shape k, scale θ and an x value.
How do I 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
Theory — what is the gamma distribution?
The gamma distribution describes positive, right-skewed quantities, such as the waiting time until several events occur or the sum of several positive waiting times. The shape parameter k affects the curve's symmetry, while the scale parameter θ determines how spread out it is along the value axis. The cumulative function uses the regularized incomplete gamma function to find the probability for any x value. In a common parameterisation, the rate β is the inverse of scale, β = 1/θ, so the two should not be confused.
Frequently asked questions
Is scale θ the same as rate?
Is a density value a probability?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.