False Positive Calculator
Calculate the false positive count from a confusion matrix and classification results.
About False Positive Calculator
False positives are negative cases incorrectly flagged as positive: FP = total_population × (1 − prevalence) × (1 − specificity). Here, (1 − prevalence) gives the number of truly negative cases, and (1 − specificity) is the false positive rate — the fraction of true negatives the test incorrectly calls positive. This is the classic 'false alarm' count, and it's why even highly specific tests can generate large numbers of false positives when screening a population where the condition is rare.
Formula
FP = total * (1 - prevalence) * (1 - specificity)
- N
- Total population
- \pi
- Prevalence (fraction truly positive)
- Sp
- Specificity (true negative rate)
Worked example
With the default values below, False Positive Calculator returns False Positives (FP) of 90.00. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Total Populationaccepts 0–1,000,000,000
- 1,000
- Prevalenceaccepts 0–1
- 0.1
- Specificityaccepts 0–1
- 0.9
Results
- False Positives (FP)
- 90.00
- Actual Negatives
- 900.00
Step by step
- 1Actual negatives: total × (1 − prevalence)= 900.00
- 2FP: actual negatives × (1 − specificity)= 90.00
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why do false positives increase when prevalence is low?
When a condition is rare, the number of true negatives in the population is very large, so even a small false-positive rate (1 − specificity) applied to that large group produces a substantial absolute number of false positives — this is the basis of the 'base rate fallacy'.
How is FP related to precision?
Precision = TP / (TP + FP), so a large FP count directly drags down precision even if the model correctly identifies most true positives, especially when the positive class is rare relative to the negative class.
What's the relationship between FP and specificity?
Specificity = TN / (TN + FP), so FP and specificity move in opposite directions — as specificity increases (fewer false alarms per true negative), FP count decreases for a fixed number of actual negatives.