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Bayes' Theorem Calculator

Posterior probability from prior and likelihoods.

Compute the posterior probability P(A|B) from the prior P(A), the likelihood P(B|A), and the false-positive rate P(B|¬A) using Bayes' theorem.

Daniel Oh By Daniel Oh
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(A|B) = P(B|A) · P(A) / [P(B|A) · P(A) + P(B|¬A) · (1 − P(A))]

In depth

Compute the posterior probability P(A|B) from the prior P(A), the likelihood P(B|A), and the false-positive rate P(B|¬A) using Bayes' theorem.