How to Calculate False Positive Rate from Confusion Matrix

False Positive Rate (FPR) Calculator

Number of negative cases incorrectly predicted as positive.

Number of negative cases correctly predicted as negative.

Calculation Results

False Positive Rate (FPR): 0

FPR as Percentage: 0%

Also known as: Probability of False Alarm or Type I Error Rate.

function calculateFPR() { var fp = parseFloat(document.getElementById('false_positives').value); var tn = parseFloat(document.getElementById('true_negatives').value); var resultBox = document.getElementById('fpr-result-box'); var fprDisplay = document.getElementById('fpr-value'); var percentDisplay = document.getElementById('fpr-percentage'); if (isNaN(fp) || isNaN(tn) || fp < 0 || tn < 0) { alert("Please enter valid non-negative numbers for FP and TN."); return; } var totalNegatives = fp + tn; if (totalNegatives === 0) { alert("The sum of False Positives and True Negatives (Total Actual Negatives) cannot be zero."); return; } var fpr = fp / totalNegatives; var fprPercent = fpr * 100; fprDisplay.innerHTML = fpr.toFixed(4); percentDisplay.innerHTML = fprPercent.toFixed(2) + "%"; resultBox.style.display = 'block'; }

Understanding the False Positive Rate (FPR)

In machine learning and statistics, the False Positive Rate (FPR) is a critical performance metric derived from a confusion matrix. It measures the proportion of actual negative instances that were incorrectly classified as positive by a model.

The FPR Formula

The formula to calculate FPR is straightforward:

FPR = False Positives (FP) / (False Positives (FP) + True Negatives (TN))

Essentially, FPR is the ratio of "False Alarms" to the "Total Actual Negatives." It is also mathematically equal to 1 – Specificity.

Why is FPR Important?

Low FPR is essential in scenarios where the cost of a false alarm is high. Consider these real-world examples:

• Medical Screening: If a test for a disease has a high FPR, many healthy people will be told they are sick, leading to unnecessary stress and invasive follow-up procedures.
• Email Spam Filters: A high FPR means important emails (Actual Negatives) are being sent to the spam folder (Predicted Positive), causing users to miss vital information.
• Security Systems: In facial recognition or intrusion detection, a high FPR results in constant false alarms, which can lead to "alarm fatigue" where real threats are ignored.

Example Calculation

Imagine a model testing 100 healthy individuals for a specific condition:

• True Negatives (TN): 90 (Correctly identified as healthy)
• False Positives (FP): 10 (Healthy people incorrectly identified as sick)

Calculation: 10 / (10 + 90) = 10 / 100 = 0.10. The False Positive Rate is 10%.

FPR vs. Precision

It is important not to confuse FPR with Precision. While Precision focuses on how many of the predicted positives were correct, FPR focuses on how many of the actual negatives were incorrectly flagged.