Statistics Calculators

Exponential Distribution Calculator

Calculate the probability density and cumulative probability of a value in an exponential distribution from a rate parameter.

Probability density —

P(X ≤ x) —

P(X > x) —

Mean (expected wait) —

About the Exponential Distribution Calculator

The exponential distribution models the waiting time between independent events that occur at a constant average rate, such as time between customer arrivals or time until a component fails.

Formula: PDF = λe⁻λᵌ · CDF = 1 − e⁻λᵌ · Mean = 1 ÷ λ

It's closely related to the Poisson distribution: if events happen at rate λ per unit time (Poisson), the time between them follows this exponential distribution. It also has the unique "memoryless" property — the probability of waiting an additional amount of time doesn't depend on how long you've already waited.