Bayes' Theorem Calculator

• Diagnostic test: enter prevalence, sensitivity and specificity to get PPV, NPV and likelihood ratios.
• General Bayes: enter a prior and two conditional probabilities to update any belief.

How common the condition is in the tested population, as a decimal — 0.01 means 1 in 100.

This prior drives the result: the rarer the condition, the more of the positive results are false.

The chance the test comes back positive when the condition is present — the true-positive rate. Higher sensitivity means fewer missed cases.

The chance the test comes back negative when the condition is absent — the true-negative rate. Its complement, 1 − specificity, is the false-positive rate.

Your belief that hypothesis A is true before seeing the evidence, as a decimal between 0 and 1.

The probability of observing the evidence B if A is true — how strongly the evidence is expected under the hypothesis.

The probability of observing B if A is false. The further apart this is from P(B | A), the more the evidence shifts your belief.