Uniform Distribution Calculator

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Uniform Distribution Calculator

The continuous uniform distribution assigns equal probability density to every value between a minimum a and a maximum b, so probability is just length over total length: P(c ≤ X ≤ d) = (d − c) ÷ (b − a). It models situations such as the arrival time of a bus known to come sometime in a 30-minute window, rounding errors, or a random number generator’s output.

Enter a and b, the probability type and the value(s). The calculator shows the density 1/(b − a), applies the length rule with values clipped to the interval, and draws the flat density with the region shaded. The mean (a + b)/2, variance (b − a)²/12 and standard deviation are reported.

As with any continuous distribution, the probability of a single exact value is zero. If your problem is a discrete uniform variable such as a fair die, each outcome simply has probability 1/(number of outcomes). For a bell-shaped alternative see the normal distribution calculator.

Frequently asked questions

What is the probability formula for a uniform distribution?

P(c ≤ X ≤ d) = (d − c) ÷ (b − a) for any sub-interval inside [a, b]. Parts of the interval outside [a, b] contribute nothing.

What are the mean and variance?

Mean = (a + b)/2 and variance = (b − a)²/12. For [0, 30] the mean is 15 and the standard deviation is 8.66.

What is the density of a uniform distribution?

A constant 1/(b − a) between a and b and zero elsewhere, so the total area is 1.

Can a uniform probability be greater than the density?

Yes; density is not probability. On [0, 0.5] the density is 2, but every probability is still between 0 and 1.

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.