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Test Accuracy (Positive Predictive Value) Calculator

Compute positive predictive value (PPV) and negative predictive value (NPV) from sensitivity, specificity and prevalence using Bayes' theorem. A per-10,000 breakdown table shows intuitively why a positive result doesn't always mean disease.

Input

Enter a test's sensitivity and specificity along with the prevalence (pre-test probability) in the target population, and Bayes' theorem reveals how likely the result is to be correct.

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Result

Positive predictive value (PPV)

15.4%

The probability that someone with a positive result truly has the disease.

Negative predictive value (NPV)

99.9 %

False positive rate (1 − specificity)

5.0 %

False negative rate (1 − sensitivity)

10.0 %

Breakdown when testing 10,000 people

Test positiveTest negativeTotal
Has disease90
True positive		10
False negative		100
No disease495
False positive		9,405
True negative		9,900
Total5859,41510,000

PPV equals "true positives ÷ total positives", and NPV equals "true negatives ÷ total negatives".

How it works

  • Enter three values — sensitivity (the share of sick people correctly flagged positive), specificity (the share of healthy people correctly flagged negative) and prevalence (the share of the target population who actually have the disease) — to gauge how reliable a test result is.
  • Positive predictive value (PPV) comes from Bayes' theorem: PPV = (sensitivity × prevalence) ÷ (sensitivity × prevalence + (1 − specificity) × (1 − prevalence)). It is the probability that a person with a positive result truly has the disease.
  • Negative predictive value (NPV) is NPV = (specificity × (1 − prevalence)) ÷ (specificity × (1 − prevalence) + (1 − sensitivity) × prevalence). It is the probability that a person with a negative result is truly healthy. The false positive rate (1 − specificity) and false negative rate (1 − sensitivity) are shown as well.
  • In low-prevalence populations, even a highly sensitive and specific test can have a sharply reduced PPV. This explains why "a positive result doesn't always mean disease", and the per-10,000 breakdown of true positives, false positives, false negatives and true negatives makes it intuitive.
  • This tool is a probability model based strictly on the values you enter; real-world sensitivity and specificity vary with the test method, thresholds and population. Note that the assumed pre-test probability (prevalence) strongly drives the result.
  • This tool provides general estimates only and is not a diagnosis or medical advice. Always consult a physician for health-related decisions.