Conditional Probability Calculator

About this calculator

This calculator applies the definition of conditional probability, P(A|B) = P(A ∩ B) / P(B): given the probability that both A and B happen together, and the probability that B happens at all, it tells you the probability of A specifically among the cases where B is already known to be true. The result is only defined when P(B) is greater than zero.

Statisticians and data analysts use this constantly — in medical testing (probability a patient has a disease given a positive test), spam filtering (probability an email is spam given it contains a certain word), and A/B testing (probability of conversion given a user saw a particular variant) — anywhere new information should update a probability estimate rather than leave it at its unconditional value.