Statistics & probability
Poisson probability calculator
Explore event-count probabilities for a supplied average rate.
A clear answer. Here’s how.
Models independent events with a constant rate in a fixed interval. Shows exact, at-most, greater-than and at-least probabilities and the model mean/standard deviation. The expected count must use the same interval as k. Uses numerical gamma functions; very small probabilities may underflow.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Expected events in the interval
- 3
- Event count k
- 2
Example result
- P(X = k)
- 0.224041807655
- P(X ≤ k)
- 0.423190081127
- P(X > k)
- 0.576809918873
- P(X ≥ k)
- 0.800851726529
- Model mean
- 3
- Model standard deviation
- 1.73205080757