basic

Poisson Distribution Probability Calculator

P(X=k) = e^(−λ)·λᵏ/k! — discrete rare events.

Calculates Poisson probabilities: P(X=k) = e^(−λ)·λᵏ/k!, and the cumulative P(X≤k) by summing from 0 to k. Used for counts of rare independent events.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X=k) = e^(−λ) · λᵏ / k!

In depth

Calculates Poisson probabilities: P(X=k) = e^(−λ)·λᵏ/k!, and the cumulative P(X≤k) by summing from 0 to k. Used for counts of rare independent events.