Beta distribution calculator
The beta distribution models continuous values from 0 to 1 and offers flexible shapes for proportions.
How to 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
The beta distribution has support [0,1]. Parameters α and β control its shape: it can be symmetric, skewed, centred or concentrated near the boundaries.
It is often used for uncertainty about proportions and probabilities. Density at a point is not point probability; probabilities are areas under the curve.
Frequently asked questions
Can f(x) exceed 1?
Yes. A density can exceed 1 while the total area under the curve remains 1.
When is beta uniform?
With α=1 and β=1 every value in [0,1] has the same density.
See also
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).
Covariance calculator
Calculate covariance for two variables, means, the cross-deviation sum and Pearson correlation.