False Positive Calculator — FPR, FDR, PPV, NPV
Enter a test's sensitivity and specificity plus the population prevalence to compute the false positive rate, false discovery rate (FDR), positive predictive value (PPV), and negative predictive value (NPV) — all via Bayes' theorem.
%
%
%
% of healthy individuals incorrectly flagged as positive = 1 − specificity
- 1
Specificity as decimal
90 ÷ 100 = 0.9 - 2
FPR (decimal)
1 − 0.9 = 0.1FPR is the complement of specificity — the fraction of healthy cases incorrectly flagged. - 3
FPR (%)
0.1 × 100 = 10
How does this calculator work?
FPR = 1 − specificity (a fixed test property). FDR = share of positive results that are wrong, calculated via Bayes: FDR = (1−prev)×FPR / ((1−prev)×FPR + prev×sensitivity). With rare conditions, FDR can be very high even for an accurate test — most positives may be false alarms.
Formula
How this is calculated
A diagnostic test has two intrinsic properties independent of the population: sensitivity (the true positive rate — how often the test is positive when the condition is present) and specificity (the true negative rate — how often the test is negative when the condition is absent). The false positive rate is simply 1 − specificity: the fraction of healthy individuals the test incorrectly flags.
However, the metrics that matter clinically — PPV and FDR — depend on how common the condition is in the population being tested (prevalence). Using Bayes' theorem: TP = prevalence × sensitivity; FP = (1 − prevalence) × (1 − specificity). PPV = TP / (TP + FP) — the probability that a positive test result reflects a true case. FDR = 1 − PPV — the fraction of positive results that are false alarms.
A key practical insight: when a condition is rare, even a highly specific test produces many false positives relative to true positives, because the large healthy population contributes many small-probability false positives that can outnumber the rare true positives. This is why confirmatory testing is essential for positive results in low-prevalence screening programs.
Frequently asked questions
FPR (= 1 − specificity) is a property of the test: the fraction of healthy individuals who test positive. FDR is a property of the positive-result pool: the fraction of positive results that are actually false alarms. FDR depends on prevalence; FPR does not.
With rare conditions, the large healthy majority produces many false positives even at high specificity. Those false positives outnumber the true positives from the small diseased minority, pulling PPV down despite excellent test accuracy.
Specificity measures only how well the test excludes negatives (TN / (TN + FP)). Overall accuracy combines all four quadrants ((TP + TN) / total), so it is inflated in low-prevalence settings where most people are truly negative.
Also known as
TG we-Calculate Editorial Team. (2026). False Positive Calculator — FPR, FDR, PPV, NPV [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/false-positive-calculator
TG we-Calculate Editorial Team. "False Positive Calculator — FPR, FDR, PPV, NPV." TG we-Calculate. 2026. https://we-calculate.com/calculator/false-positive-calculator.
TG we-Calculate Editorial Team, "False Positive Calculator — FPR, FDR, PPV, NPV," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/false-positive-calculator
@misc{wecalculate_false_positive_calculator, title = {False Positive Calculator — FPR, FDR, PPV, NPV}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/false-positive-calculator}}, year = {2026}, note = {TG we-Calculate} }
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