Determine the probability of a "Type I Error" in your detection system.
Number of incorrect alarm triggers.
Number of correctly ignored events.
Calculated Result:
The False Alarm Rate is: 0.00%
Total Negative Samples: 0
Decimal Value: 0.0000
What is the False Alarm Rate?
In statistics and signal detection theory, the False Alarm Rate (FAR)—also known as the False Positive Rate (FPR) or "fall-out"—measures the likelihood that a system will incorrectly trigger an alarm or report a positive result when no actual event or condition is present.
This metric is critical in fields such as cybersecurity (IDS/IPS), medical screening, radar detection, and manufacturing quality control. A high FAR can lead to "alarm fatigue," where users begin to ignore the system due to excessive noise.
The False Alarm Rate Formula
The calculation is based on the ratio of False Positives to the total number of actual negative events (the sum of False Positives and True Negatives).
FAR = FP / (FP + TN)
False Positives (FP): The system says "Yes" but the truth is "No".
True Negatives (TN): The system says "No" and the truth is "No".
Practical Example
Imagine a security camera designed to detect intruders. Over 24 hours:
The camera identified motion 100 times when there was no intruder (e.g., a cat or wind blowing a leaf). These are 100 False Positives.
The camera correctly remained silent during 9,900 intervals where there was no intruder. These are 9,900 True Negatives.
Using the formula: 100 / (100 + 9,900) = 100 / 10,000 = 0.01 or 1%.
Why FAR Matters for SEO and Performance
Optimizing for a low False Alarm Rate is often a trade-off with the "Recall" (Sensitivity). If you make a system too strict to avoid false alarms, you might miss real threats. Balancing these metrics is the key to creating high-performance detection algorithms.
function calculateFAR() {
var fpValue = document.getElementById('falsePositives').value;
var tnValue = document.getElementById('trueNegatives').value;
var fp = parseFloat(fpValue);
var tn = parseFloat(tnValue);
// Validation
if (fpValue === "" || tnValue === "") {
alert("Please enter values for both False Positives and True Negatives.");
return;
}
if (fp < 0 || tn < 0) {
alert("Values cannot be negative.");
return;
}
var totalNegatives = fp + tn;
if (totalNegatives === 0) {
alert("Total negative samples (FP + TN) must be greater than zero to calculate a rate.");
return;
}
// Calculation
var farDecimal = fp / totalNegatives;
var farPercentage = farDecimal * 100;
// Displaying results
document.getElementById('farDisplay').innerHTML = farPercentage.toFixed(2) + "%";
document.getElementById('totalNegativesDisplay').innerHTML = totalNegatives.toLocaleString();
document.getElementById('farDecimalDisplay').innerHTML = farDecimal.toFixed(4);
// Show result area
document.getElementById('farResultArea').style.display = "block";
// Scroll to result
document.getElementById('farResultArea').scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}