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Bayes' Theorem Calculator

Update a prior probability using a true-positive rate and false-positive rate to calculate a posterior probability.

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Posterior probability (decimal)

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Probability (%)

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Results are mathematical estimates. Statistical calculations depend on the entered data and assumptions; they do not establish causation or replace expert review.

Runs in your browser – your data never leaves your device Also available via our free API

How to use the Bayes' Theorem Calculator

  1. 1 Enter the numbers or data requested.
  2. 2 Choose the calculation option when available.
  3. 3 Review the result and its assumptions.

How the Bayes' Theorem Calculator works

Bayes’ theorem combines prior probability and evidence: posterior = sensitivity × prior / (sensitivity × prior + false-positive rate × (1 − prior)).

Entering your data

Use the values or comma-separated observations requested above. Check that you use consistent units and include every value relevant to the calculation.

Understanding the result

The result follows the formula shown here and is rounded for display. It is a mathematical aid; check assumptions and data quality before using it in coursework, analysis or a decision.

Frequently asked questions

How is this result calculated?

Bayes’ theorem combines prior probability and evidence: posterior = sensitivity × prior / (sensitivity × prior + false-positive rate × (1 − prior)).

Can I use the result as a guarantee?

No. The result depends on the inputs and stated assumptions. Review the data and method before relying on it.

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