Bayes theorem calculator

Update a prior probability with the likelihood of an observation under an event and its complement.

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Prior probability P(A)

P(B given A)

More inputs and assumptions

P(B given not A)

Answer

…

Update a prior probability with the likelihood of an observation under an event and its complement.

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Formula and assumptions

Enter probabilities from 0 to 1 for mutually exclusive A and not A. This performs probability arithmetic; it does not supply or validate the real-world probabilities you enter.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Bayes theorem calculator

Update a prior probability with the likelihood of an observation under an event and its complement.

Enter probabilities from 0 to 1 for mutually exclusive A and not A. This performs probability arithmetic; it does not supply or validate the real-world probabilities you enter.

Next: Basic calculator

A worked example

With prior probability p(a) = 0.1, p(b given a) = 0.8, p(b given not a) = 0.2, the posterior p(a given b) is 0.3076923076923077.

Before you use the result

Enter probabilities from 0 to 1 for mutually exclusive A and not A. This performs probability arithmetic; it does not supply or validate the real-world probabilities you enter.

Example results for prior probability p(a)

These examples use P(B given A): 0.8; P(B given not A): 0.2. They are reference calculations, not recommended settings.

Prior probability P(A)	Posterior P(A given B)
0.05	0.173913043478
0.1	0.307692307692
0.2	0.5

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