Poisson Distribution Calculator

Calculate probabilities for rare events occurring at a constant rate.

Average Rate (λ)

Expected number of events

Number of Events (k)

Events to calculate probability for

Distribution

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P(X = 3)

0 %

Exactly 3 events with λ = 5

P(X = 3)

P(X ≤ 3)

P(X ≥ 3)

Mean (μ)

= λ

Variance (σ²)

= λ (same as mean!)

Documentation

Poisson Distribution

The Poisson distribution models the probability of k events occurring in a fixed interval when events happen at a constant average rate λ.

PMF

Mean

Variance

Frequently Asked Questions