Bayes' Theorem Calculator interactive tool
Enter probabilities
Posterior probabilities
Updated after observing evidence B:
P(A | B)16.10%
P(not A | B)83.90%
P(B)5.90%
P(B) = P(B | A)·P(A) + P(B | not A)·P(not A).
What Is Bayes' Theorem?
A Bayes' theorem calculator helps you update the probability of a hypothesis after seeing new evidence. It takes prior probabilities P(A) and P(not A), along with likelihoods P(B|A) and P(B|not A), and returns the posterior P(A|B).
Intuition Behind Bayes' Theorem
Instead of treating probabilities as fixed, Bayes' theorem treats them as beliefs that can be updated. For example, in medical testing it reconciles a test's accuracy with how common a disease actually is to tell you the probability that a positive test result truly indicates illness. This Bayes calculator is ideal for classroom examples and quick probability sanity checks.
How To Use the Bayes' Theorem Calculator
- Enter the prior probability P(A) and P(not A) as decimals between 0 and 1, making sure they add up to 1.
- Enter the likelihoods P(B|A) and P(B|not A), representing the probability of seeing evidence B in each case.
- The Bayes theorem calculator will compute the posterior probabilities P(A|B) and P(not A|B).
- Review P(B), the total probability of the evidence, along with the updated posteriors for your hypothesis.
- Use the Example button to load a classic medical testing scenario, or Reset to clear the fields.