Bayes' Theorem Calculator
Compute the probability of disease given a positive test (PPV) from prevalence, sensitivity and false-positive rate — with full derivation.
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P(disease | positive) — PPV
16.10%
- Prior probability (prevalence)
- 1.00%
- False positives among positives
- 83.90%
How it was calculated
- 01Applying Bayes' theorem
P(D|+) = P(+|D)·P(D) / [P(+|D)·P(D) + P(+|¬D)·P(¬D)]
Basis: Bayes' theorem (P(A|B) = P(B|A)P(A)/P(B))
- 16.10%02Positive predictive value (PPV) = 16.10%
0.0095 ÷ 0.0590
Basis: Conditional probability of disease given a positive test
- 03Interpretation
Even with a positive result, the probability of actual disease is 16.10% — for rare conditions (low prior) false positives outnumber true ones, keeping PPV low
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