Poisson distribution calculator
Enter the average event count λ for a fixed interval and the event count k you want to evaluate.
Probabilities near the selected k
| k | P(X = k) |
|---|---|
| Fill in the fields above — the result is computed on this page. | |
How do I use this page?
- Enter λ for one interval.
- Enter the integer count k.
- Read the exact and cumulative probabilities.
What this page does not do: The model assumes independent events and a constant rate. Overdispersion or dependent events may require a different distribution.
Further reading
Theory — what is the Poisson distribution?
The Poisson distribution describes the number of events occurring in a fixed interval of time, space or another unit, when events happen independently at a constant average rate λ. The parameter λ is both the mean and the variance of the distribution, which sets it apart from many other discrete distributions. The calculator computes the exact probability P(X=k) for a given average λ and an event count k of interest. Note that k must be a whole number, while λ itself can be any positive value.
Frequently asked questions
Must lambda be an integer?
Why are the mean and variance equal?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.