Poisson Distribution Calculator

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Calculates probabilities for the number of events occurring in a fixed interval of time or space.

How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Average Rate of Events (λ) and Number of Desired Events (k) in the units shown.

Step 2

Read Factorial of k (k!) and Probability of k Events in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

See the inputs and their calculated results.

Average Rate of Events (λ): 5; Number of Desired Events (k): 3

Factorial of k (k!): 6; Probability of k Events: 0.1403738958

Average Rate of Events (λ): 2; Number of Desired Events (k): 1

Factorial of k (k!): 1; Probability of k Events: 0.2706705665

Average Rate of Events (λ): 10; Number of Desired Events (k): 5

Factorial of k (k!): 120; Probability of k Events: 0.0378332748

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