Poisson distribution calculator

Find event-count probabilities for a Poisson process with your expected count per interval.

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Expected count per interval

Observed count k

Answer

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Find event-count probabilities for a Poisson process with your expected count per interval.

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Formula and assumptions

Assumes independent events at a constant average rate over the same interval. Counts and expected counts are limited to 1,000; very small probabilities may underflow to zero.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Poisson distribution calculator

Find event-count probabilities for a Poisson process with your expected count per interval.

Assumes independent events at a constant average rate over the same interval. Counts and expected counts are limited to 1,000; very small probabilities may underflow to zero.

Next: Basic calculator

A worked example

With expected count per interval = 3, observed count k = 2, the probability of exactly k is 0.22404180765538775.

Before you use the result

Assumes independent events at a constant average rate over the same interval. Counts and expected counts are limited to 1,000; very small probabilities may underflow to zero.

Example results for expected count per interval

These examples use Observed count k: 2. They are reference calculations, not recommended settings.

Expected count per interval	Probability of exactly k
1.5	0.251021430167
3	0.224041807655
6	0.04461753918

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