Exponential Distribution Calculator
Work with the exponential distribution — the model for time between independent events occurring at a constant rate. Enter the rate λ (events per unit time) or the mean β = 1/λ and a value x to get the PDF, CDF, and survival P(X > x), plus the mean, median, and standard deviation; or solve the inverse: given a probability, find the waiting time. Pairs with the Poisson Distribution Calculator. Everything runs locally in your browser.
Inverse — waiting time for a probability
CDF across a range of x
The exponential distribution models waiting times: f(x) = λe−λx, F(x) = 1 − e−λx for x ≥ 0. Mean = 1/λ, median = ln 2 / λ, variance = 1/λ². It is memoryless: P(X > s+t | X > s) = P(X > t). The inverse (quantile) is x = −ln(1 − p) / λ. Pairs with the Poisson distribution (counts) — exponential is the time-between-events counterpart. Everything runs locally — nothing leaves your browser.