Poisson Distribution Calculator

Summary

Enter a mean rate (lambda) and event count (k) to compute exact and cumulative Poisson probabilities, plus a full distribution chart.

How it works

1. Enter lambda — the average number of events per interval (e.g. 3.5 calls per hour).
2. Enter k — the specific number of events you are interested in (must be a non-negative integer).
3. Click Calculate (or press Enter) to compute the three probabilities.
4. The bar chart updates to show the full Poisson PMF centered around lambda.
5. Hover over any bar to see the exact probability for that k value.
6. Adjust lambda or k and recalculate to compare scenarios instantly.

Use cases

• Estimate the likelihood of a specific number of customer arrivals per hour.
• Model the probability of rare defects in a manufacturing process.
• Predict server request spikes for capacity planning.
• Analyze the frequency of natural events such as earthquakes or meteor strikes.
• Quality-control checks: probability of k defects in a batch.
• Healthcare: probability of k emergency admissions in a given shift.
• Insurance: modeling the frequency of accident claims.
• Ecology: estimating the chance of k sightings of a rare species.

Frequently Asked Questions