False Positive Paradox Calculator
Enter a condition’s prevalence in the population along with a test’s sensitivity and specificity to see the true probability that a positive result actually reflects the condition.
What this calculator does
The false positive paradox shows that when a condition is rare, even an accurate test can produce more false positives than true positives among people who test positive. This calculator applies Bayes’ theorem to a population to reveal the real-world chance that a positive result actually means someone has the condition.
How the calculation works
Starting from the population size and prevalence, the calculator finds how many people actually have the condition and how many do not. Sensitivity (the true positive rate) determines how many of the affected people test positive, while specificity (the true negative rate) determines how many unaffected people correctly test negative — the rest of the unaffected group become false positives. The positive predictive value (PPV) is then true positives divided by all positive test results: PPV = TP / (TP + FP).
When prevalence is low, the much larger unaffected group can generate more false positives than the smaller affected group generates true positives, even with a highly accurate test. This tool illustrates a general statistical concept for educational purposes and is not a substitute for professional interpretation of any specific test result.