Tools/Bayes' Theorem Calculator

Bayes' Theorem Calculator

Start with a prior probability and update it with one or more independent pieces of evidence. Includes medical-test and spam-filter presets with sensitivity / false-positive rate inputs.

Setup

Preset Prior P(H) P(E|H) — sensitivity (true positive rate) P(E|¬H) — false positive rate (1 − specificity) Number of independent positive tests

Posterior trajectory

Sequential update table

After test #	P(H\|E)	LR	Posterior odds

Why this exists

Almost no popular explanation of "Bayes' theorem" answers the actual question most people have: if I have a positive test result, what's the chance I actually have the disease? The answer depends on the prior (how common the disease is) and the test's false-positive rate, not just its sensitivity.

Classic example: 1% disease, 95% sens, 90% spec

Of 10,000 people, 100 have the disease. Test catches 95 of them. Of 9,900 healthy, 10% = 990 false-positive. Total positives: 1,085. Only 95 are true positives. So P(disease | positive) = 95/1085 ≈ 8.76%. Counter-intuitive, but real.

Who uses it

Doctors and epidemiologists interpreting screening results.
Data scientists calibrating classifiers.
Anyone arguing with a friend about base rates.

Limitations

Assumes test results are conditionally independent given H. In reality, repeat tests of the same kind often aren't independent (same lab, same systematic bias).
Uses fixed sensitivity / specificity. Real tests vary by patient subgroup.
Not a substitute for professional medical or statistical advice.