Poisson Distribution Calculator
Probability of k events in an interval.
Enter your values
ⓘ Live results
Results
- P(X = k)
- 0.104196
- P(X ≤ k)
- 0.889326
- P(X > k)
- 0.110674
- Mean and variance
- 4
- Standard deviation
- 2
Quick answer
The Poisson distribution models rare independent events at a constant average rate λ over a fixed interval.
P(X=k) = λ^k e^(−λ) / k!
How to use the Poisson Distribution Calculator
- 1Enter the average number of events per interval.
- 2Enter the event count you are testing.
- 3Read exact and cumulative probabilities.
Worked example
Using the values the calculator loads with:
Inputs
- Average rate λ4
- Number of events k6
Results
- P(X = k)0.104196
- P(X ≤ k)0.889326
- P(X > k)0.110674
- Mean and variance4
- Standard deviation2
Frequently asked questions
When is Poisson appropriate?
Independent rare events at a steady rate: calls per hour, defects per metre.
How does it relate to binomial?
Poisson is the limit of binomial when n is large and p is small.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.