Uniform Distribution Calculator

About this calculator

The continuous uniform distribution on an interval [a, b] describes a quantity that is equally likely to take any value in that range, with no value more probable than another. Its probability density function (PDF) is flat, equal to 1/(b − a) everywhere between a and b and zero outside it, its mean is simply the midpoint (a + b)/2, and its variance is (b − a)² / 12.

The cumulative distribution function (CDF) at a point x gives the probability that the random variable is less than or equal to x, calculated as (x − a)/(b − a) within the interval. This distribution is the standard model for situations where outcomes really are equally likely across a range, such as rounding errors, the position where a random point lands on a line segment, or the output of a basic pseudo-random number generator before it's transformed into other distributions, and it's a foundational building block taught early in probability courses.

Enter the interval [a, b] and a point x, and this calculator returns the distribution's mean, variance, and the PDF and CDF value at x.