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Poisson PMF / CDF Expected Value Calculator

P(X=k) = e^(−λ)λ^k/k! — probability of k events in interval.

Calculates Poisson probability mass function P(X = k) and cumulative distribution P(X ≤ k) for a given rate λ and event count k.

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) × λ^k / k!; E[X] = λ; Var = λ

In depth

Calculates Poisson probability mass function P(X = k) and cumulative distribution P(X ≤ k) for a given rate λ and event count k.