basic

Bayes' Theorem Posterior Probability Calculator

P(A|B) = P(B|A)·P(A) / P(B) — inverse probability.

Applies Bayes' theorem: P(H|E) = P(E|H)·P(H) / [P(E|H)·P(H) + P(E|¬H)·P(¬H)]. Used in medical testing, spam filtering, and decision analysis.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(H|E) = P(E|H)·P(H) / [P(E|H)·P(H) + P(E|¬H)·(1−P(H))]

In depth

Applies Bayes' theorem: P(H|E) = P(E|H)·P(H) / [P(E|H)·P(H) + P(E|¬H)·P(¬H)]. Used in medical testing, spam filtering, and decision analysis.