Exponential Distribution Calculator
Calculate exponential distribution probabilities, mean time between events, and survival probabilities with interactive visualization.
The exponential distribution models the time between independent events that occur at a constant average rate. It is the continuous counterpart of the Poisson distribution and the simplest model for waiting times, component lifetimes, and inter-arrival gaps.
Use this calculator to compute the probability of an event occurring within a given time, find mean time between failures, and visualize the memoryless decay of the survival function.
Launch the Exponential Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhat does the memoryless property mean?
It means the probability of waiting an additional time t is the same regardless of how long you have already waited. Formally, P(X > s + t | X > s) = P(X > t).
How is the exponential distribution related to Poisson?
If events follow a Poisson process with rate λ, the time between consecutive events follows an exponential distribution with the same rate parameter λ.
How do I calculate mean time between failures?
The mean of the exponential distribution is 1/λ. Set the rate parameter to your observed failure rate and the mean gives the expected time between failures.