The False Positive Rate (FPR) Calculator helps determine the likelihood that a test or prediction incorrectly labels a negative result as positive. This is especially important in fields such as healthcare, cybersecurity, and artificial intelligence, where decisions depend on the precision of results.
In practice, a high FPR can lead to unnecessary actions, costs, or stress—like false alarms in security systems or unnecessary treatments in medical diagnoses. Using this calculator allows users to assess and minimize these risks.
This tool belongs to the Diagnostic Accuracy and Statistical Error Analysis Calculators category.
formula of False Positive Rate Calculator
Primary Formula for FPR:
False Positive Rate = False Positives / (False Positives + True Negatives)
Where:
- False Positives (FP): Number of cases wrongly marked as positive
- True Negatives (TN): Number of correct negative predictions
Alternative Form (using specificity):
FPR = 1 − Specificity
Supporting Metrics for Context:
True Positive Rate (TPR) = True Positives / (True Positives + False Negatives)
Specificity = True Negatives / (True Negatives + False Positives)
These related formulas help you understand the full scope of prediction accuracy.
Reference Table: Estimated FPR Scenarios
| False Positives (FP) | True Negatives (TN) | FPR (Decimal) | FPR (%) |
|---|---|---|---|
| 5 | 95 | 0.050 | 5% |
| 10 | 90 | 0.100 | 10% |
| 20 | 80 | 0.200 | 20% |
| 15 | 135 | 0.100 | 10% |
| 50 | 950 | 0.050 | 5% |
This table gives a quick overview of how often false positives may occur relative to the total number of actual negative cases.
Example of False Positive Rate Calculator
Imagine a cancer screening test is applied to 1,000 patients. Out of these:
- 50 people do not have cancer but test positive (false positives)
- 950 people are correctly shown as cancer-free (true negatives)
Now apply the formula:
FPR = 50 / (50 + 950) = 50 / 1000 = 0.05 or 5%
This means that for every 100 people who don’t have cancer, 5 might still get a positive result by mistake.
Most Common FAQs
Because it tells us how often healthy individuals are wrongly diagnosed, leading to unnecessary anxiety or treatment. Lowering FPR improves test reliability.
No. FPR focuses on negatives being misclassified as positives. False Discovery Rate (FDR) looks at how many of the positive results are actually incorrect.
You can improve the quality of training data, apply better feature selection, or fine-tune classification thresholds to reduce FPR in predictive models.