Beta Distribution Calculator
Calculate beta distribution probabilities for proportions, rates, and Bayesian priors with interactive PDF and CDF visualization.
The beta distribution is the standard model for random variables bounded between 0 and 1, making it ideal for proportions, probabilities, and rates. Its two shape parameters give it remarkable flexibility, from uniform to U-shaped to highly concentrated around any value in the unit interval.
Use this calculator to compute interval probabilities for conversion rates, model prior beliefs in Bayesian analysis, and explore how the alpha and beta parameters control skewness and concentration.
Launch the Beta Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhen should I use a beta distribution?
Use it whenever your variable is a proportion or probability bounded between 0 and 1, such as conversion rates, click-through rates, or success probabilities in A/B testing.
How do alpha and beta relate to observed data?
In Bayesian analysis, if you start with a Beta(α, β) prior and observe s successes in n trials, the posterior is Beta(α + s, β + n − s). The parameters can be interpreted as pseudo-counts.
What happens when alpha and beta are both 1?
Beta(1, 1) is the uniform distribution on [0, 1], representing no prior preference for any value in the interval.