Poisson Count Probability Calculator
Find the probability of an exact event count for a constant-rate Poisson model.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Poisson Count Probability Calculator
Use the expected count for the entire interval, not a rate per another time unit. A Poisson model assumes independent arrivals and a constant expected rate.
The calculation
Worked example
An expected count of four gives a 14.6525% probability of exactly two events in that interval.
Assumptions and limits
Bursting, clustering and changing arrival rates may invalidate the model. The calculator supports mean counts up to 700 and does not infer the rate from observations.
Common questions
Which inputs should I use?
Use the expected count for the entire interval, not a rate per another time unit. A Poisson model assumes independent arrivals and a constant expected rate.
What does the result exclude?
Bursting, clustering and changing arrival rates may invalidate the model. The calculator supports mean counts up to 700 and does not infer the rate from observations.