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Statistics

Poisson Probability Calculator

Find the probability of exactly k events for a constant-rate Poisson model.

Data stays on this deviceConvention explained below
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Check the dataset and sample convention before interpreting results.

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Your result

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Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter expected events, observed events.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
Expected eventsNumeric value. Zero or positive. Maximum: 1000.3
Observed eventsWhole numbers only. Zero or positive. Maximum: 1000.2

Result for these sample inputs

0.224041808 probability

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

P(X = k) = exp(−λ) λ^k/k!.

A WORKED EXAMPLE

Using expected events = 3, observed events = 2, the result is 0.224041808 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Methodology maintained by ClarityKit. How these tools are built and checked.