Statistics Calculators

Poisson Distribution Calculator

Calculate the probability of a given number of events occurring in a fixed interval, based on the average event rate.

P(X = k) —

P(X ≤ k) —

Mean (λ) —

Standard deviation —

About the Poisson Distribution Calculator

The Poisson distribution models the number of times a rare, independent event happens within a fixed interval of time or space, given only the average rate at which it occurs — such as customer arrivals per hour or typos per page.

Formula: P(X = k) = (e⁻λ × λᵌ) ÷ k! · Mean = λ · Standard deviation = √λ

Unlike the binomial distribution, the Poisson distribution doesn't need a fixed number of trials — only the average rate (λ) and the interval, making it useful for modeling rare, randomly occurring events.