Uniform Distribution Calculator
Calculate uniform distribution probabilities for continuous and discrete uniform variables with interactive PDF and CDF charts.
The continuous uniform distribution assigns equal probability density to every value in a closed interval [a, b]. It is the simplest continuous distribution and serves as the baseline model for complete uncertainty within a bounded range, random number generation, and simulation.
Use this calculator to compute interval probabilities, explore the flat PDF, and see how the CDF rises linearly from a to b. The uniform distribution is also fundamental to inverse transform sampling used in Monte Carlo methods.
Launch the Uniform Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhen should I use a uniform distribution?
Use it when all values in an interval are equally likely, such as rounding errors, random number generation, or as a non-informative prior in Bayesian analysis.
How do I compute P(c ≤ X ≤ d) for a uniform distribution?
For Uniform(a, b), the probability is simply (d − c) / (b − a), as long as [c, d] is within [a, b]. Use the interval tool for automatic computation.
What is the variance of a uniform distribution?
The variance is (b − a)² / 12. It depends only on the width of the interval, not on where the interval is centered.