The Equal Error Rate (EER) Calculator is a tool used to evaluate the accuracy of biometric systems, classifiers, or verification models. It helps determine the threshold at which the False Acceptance Rate (FAR) and False Rejection Rate (FRR) are equal. This point reflects a balance between the likelihood of incorrectly accepting an impostor and wrongly rejecting a legitimate user.
EER is especially important in fields like fingerprint recognition, facial verification, and voice-based identification where system performance needs to be both secure and user-friendly. A lower EER means the system performs better, reducing errors on both sides.
Formula of Equal Error Rate Calculator
1. Equal Error Rate Formula (Conceptual)
There is no single algebraic formula for EER. It is found where the following condition is met:
FAR(threshold) = FRR(threshold)
This is identified by checking error rates across a range of thresholds and finding the point where the two rates intersect or are closest.
2. Step-by-Step Calculation
To compute EER:
- Collect similarity scores or decision values for genuine and impostor attempts.
- Set a range of thresholds across the score spectrum.
- At each threshold, calculate:
False Acceptance Rate (FAR):
FAR = False Accepts / Total Impostor Attempts
False Rejection Rate (FRR):
FRR = False Rejects / Total Genuine Attempts
- Identify the threshold where FAR and FRR are approximately equal.
- The EER is the value of FAR (or FRR) at that threshold.
3. Units
EER is typically expressed as a percentage (%). A system with an EER of 2% is more accurate than one with an EER of 5%.
Useful Reference Table
| Threshold | FAR (%) | FRR (%) |
|---|---|---|
| 0.1 | 0.1 | 95.0 |
| 0.3 | 1.5 | 70.0 |
| 0.5 | 5.0 | 30.0 |
| 0.7 | 10.0 | 10.0 ← EER point |
| 0.9 | 25.0 | 2.0 |
From the table, the Equal Error Rate is 10% at threshold 0.7.
Example of Equal Error Rate Calculator
Imagine a facial recognition system tested with 100 impostor attempts and 100 genuine attempts. After running the system at various thresholds:
- At threshold 0.6:
- 10 impostors were accepted (FAR = 10/100 = 10%)
- 10 genuine users were rejected (FRR = 10/100 = 10%)
Here, FAR = FRR, so the EER = 10%.
This tells us the system has moderate accuracy. Lowering the EER would improve security and user satisfaction.
Most Common FAQs
A low EER means the system is highly accurate, making fewer mistakes on both false acceptances and rejections.
EER shows how well a system balances security and usability. It’s a reliable single metric for system performance.
Yes, different datasets, environmental factors, and user behavior can affect the EER of a system.