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Statistics

Beta Distribution Calculator

Evaluate cumulative probability for a beta distribution on the unit interval.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter shape alpha, shape beta, value x.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

CDF is the regularized incomplete beta I_x(alpha,beta); mean = alpha/(alpha+beta).

A WORKED EXAMPLE

Using shape alpha = 2, shape beta = 2, value x = 0.5, the result is 0.5. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Main result is P(X≤x). Both shape parameters must be positive; numerical convergence is checked, but this does not fit parameters to data.

What to keep in mind

Main result is P(X≤x). Both shape parameters must be positive; numerical convergence is checked, but this does not fit parameters to data. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this beta distribution calculator?

Evaluate cumulative probability for a beta distribution on the unit interval. Enter shape alpha, shape beta, value x. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Main result is P(X≤x). Both shape parameters must be positive; numerical convergence is checked, but this does not fit parameters to data.

Methodology maintained by ClarityKit. How these tools are built and checked.