Bayes’ Theorem Calculator
Update a probability with new evidence using Bayes’ theorem, one of the core tools of statistical reasoning.
What Bayes’ theorem does
Bayes’ theorem tells you how to update the probability of an event (A) after observing new evidence (B). It combines what you believed before the evidence (the prior) with how likely that evidence is under different scenarios (the likelihoods) to produce an updated, more informed probability (the posterior).
The formula
The calculator applies P(A|B) = [P(B|A) × P(A)] / P(B), where P(B) is expanded as P(B|A)×P(A) + P(B|not A)×P(not A). Enter your prior belief about how common A is, how often B correctly signals A (the true positive rate), and how often B occurs even when A is false (the false positive rate).
This calculator is widely used to reason about test results, filters, and screening scenarios where a rare event and an imperfect signal are involved. It is provided for general educational and planning purposes and does not replace professional statistical, medical, or legal analysis.