Poisson Distribution Calculator

Calculate Poisson probabilities for event counts given an average rate λ.

The average number of events in the interval. Must be positive. Example: 3.5 calls per hour.
The specific number of occurrences to compute probability for.

Results

P(X = k)
P(X ≤ k)
P(X ≥ k)
P(X < k)
P(X > k)
Mean = λ
Variance = λ
Std Dev = √λ

Formula

P(X=k) = e^(−λ) × λ^k / k!
References: Poisson distribution: P(X=k) = e^(-λ)λ^k/k!. Mean = Variance = λ. Named after Siméon Denis Poisson (1837). Uses log-space for numerical stability.