Bayes' Theorem Calculator

Update a probability in light of new evidence with Bayes' theorem. Enter the prior P(A), the sensitivity P(B|A), and the false-positive rate P(B|¬A); the tool computes the posterior P(A|B) after observing B, the posterior after a negative result P(A|¬B), the marginal P(B), and a natural-frequency breakdown. Supports repeating an independent test. Everything runs locally in your browser.

Inputs

Prior P(A)

Sensitivity P(B|A)

False-positive rate P(B|¬A)

Repeated independent tests (positive)

Posterior

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Natural frequencies (per 10,000)

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Bayes' theorem relates the conditional probabilities: P(A|B) = P(B|A)·P(A) / P(B), where P(B) = P(B|A)·P(A) + P(B|¬A)·P(¬A) is the total probability of the evidence. The posterior is how likely A is after seeing B — famously, even a highly sensitive test for a rare disease yields a low posterior because the false positives outnumber true positives. In odds form, posterior odds = prior odds × likelihood ratio, where LR = P(B|A)/P(B|¬A); repeating an independent test multiplies the odds by LR each time. Pairs with the Statistics Calculator and Confidence Interval tools. Everything runs locally — nothing leaves your browser.