Poisson Distribution Calculator
Compute Poisson probabilities from a mean rate λ, with the PMF charted.
What is Poisson Distribution?
The Poisson distribution counts events that happen independently at a constant average rate λ in a fixed interval — calls per hour, defects per batch, particles per second. Its defining feature is that the mean and the variance are both λ.
How it works
P(X = k) = e^−λ · λᵏ ÷ k! is evaluated through a log-gamma so large k does not overflow, and the tails are summed from the same terms. The near terms are drawn as a bar chart, and the mean-equals-variance identity is stated because it is how a real data set is tested for plausibility.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.