False Positive Rate (FPR) Calculator
Calculate the probability of a "false alarm" based on test performance metrics.
Calculated Results
False Positive Rate (FPR): 0%
How to Calculate False Positive Rate
In medical testing, machine learning, and statistical hypothesis testing, the False Positive Rate (FPR) represents the probability that the test triggers a "positive" result for an individual or sample that is actually "negative." This is also known as a Type I error or a "false alarm."
The Formula for FPR
While people often ask how to calculate FPR from both sensitivity and specificity, the mathematical reality is that FPR is derived directly from Specificity. Sensitivity (the True Positive Rate) describes how well the test finds the "positives," but it does not influence the "false positive" count among the "negatives."
False Positive Rate (FPR) = 1 – Specificity
Definitions and Relationships
- Specificity (True Negative Rate): The ability of a test to correctly identify those without the condition. If a test has 90% specificity, it correctly identifies 90 out of 100 healthy people.
- Sensitivity (Recall / True Positive Rate): The ability of a test to correctly identify those with the condition.
- The Relationship: FPR and Specificity always add up to 1 (or 100%). If your specificity is 95%, your False Positive Rate is 5%.
Step-by-Step Calculation Example
Imagine a diagnostic test for a specific virus:
- Determine Specificity: The lab reports the test has a Specificity of 98%.
- Apply the Formula: FPR = 100% – 98%.
- Result: The False Positive Rate is 2%. This means that for every 100 people who do NOT have the virus, 2 will receive a positive test result incorrectly.
FPR in the Confusion Matrix
| Metric | Calculation Formula |
|---|---|
| False Positive Rate | FP / (FP + TN) |
| Specificity | TN / (TN + FP) |
| Sensitivity | TP / (TP + FN) |
Why Sensitivity is Included in This Context
Though Sensitivity is not used to calculate the FPR itself, the two metrics are used together to create a Receiver Operating Characteristic (ROC) Curve. The ROC curve plots Sensitivity (Y-axis) against FPR (X-axis). A perfect test would have 100% Sensitivity and 0% FPR, appearing in the top-left corner of the graph.