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Uniform Distribution Calculator

Probability, mean, variance and percentiles of a continuous uniform distribution between a and b, including P(x₁ ≤ X ≤ x₂).

Lower bound (a)

Upper bound (b)

From x₁

To x₂

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How it works

P(x₁ ≤ X ≤ x₂) = (x₂ − x₁) ÷ (b − a) · mean = (a+b)/2 · Var = (b−a)²/12

A continuous uniform distribution spreads probability evenly across an interval, so probability is simply the fraction of the interval covered. It is the model behind random-number generators, rounding error and “arrives sometime between 2 and 3 pm” problems.

Worked example

Bus arrives uniformly between 0 and 10 minutes: P(wait between 2 and 6.5 min) = 4.5/10 = 0.45; mean wait 5 min; SD 2.89 min.

Frequently asked questions

What is the probability of exactly one value?

Zero for a continuous distribution — only intervals carry probability.

Discrete uniform (like a die)?

For n equally likely outcomes each has probability 1/n, mean (n+1)/2 and variance (n²−1)/12.

Related calculators

Normal Distribution Calculator

Find the probability that a normally distributed value falls below or above a point — with its z-score and probability density.

Expected Value Calculator

Compute the expected value of a discrete probability distribution from its outcomes and probabilities — with the variance and standard deviation.

Random Number Generator

Generate random numbers in any range: whole numbers or decimals, one or up to 1,000 at a time, with or without repeats, numbers to exclude, sorted or in draw order, and an optional seed to repeat a draw. Good for raffles, giveaways, games and sampling.

For education — check assumptions (sample size, distribution) before using statistics in real decisions.