Statistics Calculators

Uniform Distribution Calculator

Calculate the probability density, interval probability, mean and standard deviation of a continuous uniform distribution.

Probability density (constant) —

P(lower ≤ X ≤ upper) —

Mean —

Standard deviation —

About the Uniform Distribution Calculator

A continuous uniform distribution describes a value that is equally likely to fall anywhere between a minimum (a) and maximum (b), with no values more likely than others — the classic "flat" distribution.

Formula: PDF = 1 ÷ (b − a) · Mean = (a + b) ÷ 2 · Variance = (b − a)² ÷ 12

The probability of landing in any sub-interval is simply that interval's width divided by the full range's width. Uniform distributions are the basis of random number generators and are used to model situations where any outcome in a range is equally plausible.