Poisson Distribution Calculator

Find Poisson probabilities for an average event rate and a count of events.

Poisson probabilities

Probability

Probability: —

Mean: — · Variance: —

Standard deviation: —

Cumulative up to k: —

The Poisson model suits counts of independent events over a fixed interval at a steady average rate.

Enter the average number of events in the interval you are studying.
Choose the probability you want and set the event count or counts.
Read the probability, mean, variance and standard deviation in the result panel.

Common questions about the free online poisson distribution calculator.

Enter the average number of events and the count you are interested in, then choose an exact or cumulative probability.

It models how many times an event happens in a fixed interval when events occur independently at a steady average rate.

Lambda is the average number of events in the interval, and it is also the mean and the variance of the distribution.

Use Poisson for counts of rare events over time or space, such as calls per hour, when there is no fixed number of trials.

The probability of k events is e to the power minus lambda times lambda to the power k, divided by k factorial.

For a Poisson distribution the standard deviation is the square root of lambda, so it grows more slowly than the mean.

Yes. Rates such as 2.5 events per hour are common, and the calculator accepts any positive average rate.

It shows the chance of observing up to and including the first count you entered, whatever probability mode is selected.

No. Every calculation runs locally in your browser, so your numbers never leave your device.

Yes. It is completely free and unlimited, with no account, no sign-up and no usage limits of any kind.

Last updated: October 10, 2026