Poisson Distribution Calculator

Calculate probabilities for events occurring in a fixed interval using the Poisson distribution. Perfect for analyzing rare events and counting processes.

Parameters

Lambda (average rate)*

Number of Events (k)*

Poisson Distribution Results

Probability Mass (PDF)

0.1404

This is the probability of exactly 3 events occurring when the average rate is λ = 5.0.

Cumulative Probability (CDF)

0.2650

This is the probability of 3 or fewer events occurring (P(X ≤ 3)).

Interpretation: With a lambda (average rate) of λ = 5.0, there's a 14.04% chance of observing exactly 3 events, and a 26.50% chance of observing 3 or fewer events.

Probability Distribution

Parameters

Lambda (average rate)*

Number of Events (k)*

How to Use Poisson Calculator

Enter lambda (average rate of events)
Specify number of events
View probability results and distribution

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by @scottpaulin