Poisson Distribution Calculator

Enter an average event count and observed count to calculate exact and cumulative probabilities plus distribution summaries.

Average event count (λ)

Observed events (k)

—P(X = k)

—P(X ≤ k)

—P(X ≥ k)

—Standard deviation

—For a Poisson distribution, mean and variance both equal λ.

How to use this Poisson Distribution Calculator

Calculate Poisson probabilities from an expected event rate. Enter your values above and the result is calculated directly in your browser. No account is required.

Fast answer, clear inputs

This tool is built around one job: give the answer quickly without forcing a signup or hiding the result. Related tools are linked nearby when the next calculation or conversion is useful.