Beta distribution calculator
The beta distribution models continuous values from 0 to 1 and offers flexible shapes for proportions.
How do I use this page?
- Choose density, CDF, upper tail or quantile.
- Enter positive α and β.
- Provide x in [0,1] or probability q.
What this page does not do: The model applies to continuous values from 0 to 1. The parameters are not automatically counts of successes and failures without a stated statistical model.
Further reading
Theory — what is the beta distribution?
The beta distribution models continuous values between 0 and 1, making it a natural tool for describing proportions and probabilities. Parameters α and β control the shape of the curve — it can be symmetric, skewed, or concentrated near the middle or the edges of the interval. The density f(x) is not limited to values below 1 — it can exceed 1, since only the total area under the curve must equal 1. This distribution is often used as a prior in Bayesian analysis.
Frequently asked questions
Can f(x) exceed 1?
When is beta uniform?
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.