Poisson Distribution Calculator
Compute Poisson probabilities for event counts per interval using lambda with PMF and CDF visualization.
The Poisson distribution models the number of events in a fixed interval when events occur independently at an average rate λ.
This page lets you compute exact and cumulative probabilities for count outcomes and inspect how λ changes the distribution shape.
Launch the Poisson Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhat does λ mean in a Poisson model?
λ is the expected number of events in the interval and is both the mean and variance of the distribution.
Can Poisson approximate binomial?
Yes, when n is large and p is small, with λ = n·p, Poisson is often a practical approximation.
Is this useful for queueing and reliability?
Yes. Poisson models are common for arrivals, failures, and incident counts per unit time or area.