Poisson Distribution Calculator
The Poisson distribution models the number of events in a fixed interval when events happen at a constant average rate λ, independently. Enter λ and a target k to get the point probability, the cumulative probabilities and the (equal) mean and variance.
Worked examples
Frequently asked questions
When does Poisson apply?
When events occur independently at a constant average rate, and the count over a fixed window is what you want to model — calls to a help line per hour, photons per second, defects per metre.
Why are the mean and variance both λ?
It is a defining property of the Poisson distribution. The standard deviation is therefore √λ — variability grows as the square root of the rate.
How does Poisson relate to Binomial?
Poisson(λ) is the limiting case of Binomial(n, p) as n → ∞ and p → 0 with n·p = λ held fixed. So it approximates rare events over many trials.