📊 Beta Distribution Calculator
Explore the beta distribution by entering its two shape parameters to get the mean, variance, and density at a chosen point.
What the beta distribution describes
The beta distribution models random variables that are bounded between 0 and 1, such as proportions, rates, or probabilities themselves. Its shape is controlled by two positive parameters, alpha and beta, which determine whether the distribution is skewed toward 0, toward 1, symmetric, or U-shaped.
How this calculator works
Enter alpha and beta to find the distribution’s mean (alpha / (alpha + beta)) and variance. Enter a point x between 0 and 1 to see the probability density function (PDF) value there, calculated using the beta function B(alpha, beta) computed via the gamma function. If both alpha and beta are greater than 1, the calculator also reports the mode, the single most likely value.
The beta distribution is widely used in statistics for modeling uncertainty about proportions, including in Bayesian analysis. This tool is provided for general educational and analytical use.