📈 Poisson Distribution Calculator
Enter the average number of events expected in an interval (lambda) and a target count to calculate the Poisson probability of that many events occurring.
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What is the Poisson Distribution?
The Poisson distribution models the number of times a rare, random event happens in a fixed interval of time or space, when events occur independently and at a known average rate — like customer arrivals per hour or typos per page.
The Formula
P(X=k) = (e^(−λ) × λ^k) / k!, where λ (lambda) is the average number of events per interval and k is the number of events you’re checking the probability of. Both the mean and variance of a Poisson distribution equal λ.
- “At least” and “at most” sum the individual probabilities across the relevant range of k values.
- Lambda must be zero or greater.
Provided for general statistical education and planning purposes.
Last reviewed August 2026