How it works
P(X=k) = e^−λ × λ^k / k!, evaluated using logarithms.
Input definitions
- Mean events per interval (0–1000)
- Enter the value in the labeled unit.
- Event count (0–2000)
- Enter the value in the labeled unit.
A worked example
- Mean events per interval (0–1000)
- 2
- Event count (0–2000)
- 3
Assumptions & limits
Independent arrivals at a constant average rate; exact-count probability only. Extreme tails can underflow.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
When should I use Poisson instead of binomial?
Poisson models a count of independent arrivals in a fixed interval with a constant mean rate. Binomial models successes in a fixed number of independent trials with a fixed success probability.
Why can statistical results differ between tools?
Denominator, interpolation and boundary conventions can differ. Use the method and assumptions on this page to compare the same definition; displayed decimals may also be rounded.
How does the Poisson event probability tool work?
P(X=k) = e^−λ × λ^k / k!, evaluated using logarithms.
What are the assumptions and limits of Poisson event probability?
Independent arrivals at a constant average rate; exact-count probability only. Extreme tails can underflow.