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Statistics

Poisson Probability Calculator

Calculate exact and cumulative Poisson event probabilities.

Last validated: 2026-02-14

Use this free online Poisson Probability Calculator to evaluate probabilities for event counts over fixed intervals with known average rate. It is useful for analysis, reporting, coursework, and experiment planning when you need quick statistical evidence without building a spreadsheet. The form focuses on Lambda (expected events), k (event count) and returns Poisson Inputs, Result, so you can move from input to answer without setting up a spreadsheet or custom script. Run one realistic example, adjust the inputs, and compare how the result changes before you copy or share it. Treat the result as a statistical aid: sample quality, independence, distribution assumptions, and context still determine whether the conclusion is valid.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Poisson Inputs

Result

P(X = k): 0.1849589735

P(X ≤ k): 0.3208471989

How to use this tool

  1. Enter Lambda (expected events), k (event count) for the poisson probability calculator, keeping units, dates, or text format consistent with the form labels.
  2. Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
  3. Click "Run the tool" and review Poisson Inputs, Result for the primary output.
  4. Check the statistical assumptions and sample context before using the result in a report or decision.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

  • Lambda: 3.5
  • K: 2

Expected Outputs

  • Lambda: 3.5
  • K: 2
  • Exact probability: 0.184959
  • Cumulative probability: 0.320847

Interpretation

Confidence and limitations

Formula References

Assumptions

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