Sensitivity specificity calculator: compute sensitivity, specificity, PPV and NPV from any 2x2 confusion matrix. Free, runs in your browser, no signup.
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General estimate for planning only — not medical advice. Consult a doctor about your specific situation.
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These tools provide general estimates for planning and education only.
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Worked example: a 200-patient validation study
Suppose a new rapid test is checked against a reference standard on 200 patients: 45 true positives, 10 false negatives, 10 false positives, and 140 true negatives. Sensitivity is TP divided by everyone who actually has the condition: 45 / (45 + 10) = 45 / 50 = 90.0%. Specificity is TN divided by everyone who does not: 140 / (140 + 10) = 140 / 150 = 93.3%.
The predictive values use the opposite denominators. PPV is TP over everyone who tested positive: 45 / (45 + 10) = 45 / 55 = 81.8%. NPV is TN over everyone who tested negative: 140 / (140 + 10) = 140 / 150... but note the false negatives shift this: 140 / (140 + 10) would double-count; the correct NPV denominator is 140 + 10 false negatives = 145, giving 140 / 145 = 96.6%. So a negative result is fairly trustworthy here, while a positive result is wrong nearly 1 in 5 times.
The calculator returns exactly these four numbers from your four counts. If you enter the same 45, 10, 10, 140, the hero value reads 90.0% sensitivity with specificity 93.3%, PPV 81.8%, NPV 96.6%. Any zero or negative count, or all four fields empty, triggers the check-the-inputs message instead.
Why PPV collapses when the condition is rare
Sensitivity and specificity belong to the test; PPV and NPV belong to the population. Run the same 90.0% / 93.3% test where prevalence is 1% and the picture flips. Out of 10,000 people, 100 have the condition: 90 are caught (TP) and 10 are missed (FN). Of the 9,900 without it, 9,300 test negative (TN) and 600 test positive (FP).
PPV is now 90 / (90 + 600) = 90 / 690 = 13.0%. More than 85% of positive results are false alarms, even though the test itself did not change. NPV barely moves: 9,300 / (9,300 + 10) = 99.9%. This is the base-rate effect that makes broad screening of rare conditions produce floods of follow-up testing: the same 90/93.3 numbers that looked reassuring in a 200-patient clinic sample are weak evidence on their own at population scale.
Two practical consequences: never compare PPVs from studies with different prevalence, and when validating a test, sample cases and controls deliberately (as a 50/50 enrichment does) so the sensitivity and specificity estimates are stable, then report predictive values separately for each real-world prevalence you care about.
