False Positive Rate (FPR) Calculator
Calculate the false positive rate (FPR) from false positive and true negative counts.
Inputs
False Positive Rate
0.02%
Specificity (1 − FPR)
0.98%
Step by step
FPR: FP / (FP + TN)
20 ÷ (20 + 850)
= 0.0230
Specificity: 1 − FPR
1 − 0.0230
= 0.9770
How it works
The false positive rate (FPR) measures how often the model incorrectly flags a true negative as positive: FPR = FP / (FP + TN) = 1 − specificity. It's the x-axis of the ROC curve, representing the 'cost' side of the sensitivity/specificity tradeoff — as a model's decision threshold is lowered to catch more true positives, FPR typically rises as well, since more true negatives get swept up as false alarms.
Formula
FPR = FP / (FP + TN)
- FP
- False positives
- TN
- True negatives
Frequently Asked Questions
How is FPR used in the ROC curve?
The ROC curve plots true positive rate (sensitivity) on the y-axis against false positive rate on the x-axis across every possible classification threshold, visualizing the full tradeoff between catching positives and generating false alarms.
What's a 'good' FPR?
It depends entirely on context — for high-stakes false alarms (e.g. locking out a legitimate user), you want FPR very close to 0; for low-stakes screening where follow-up review is cheap, a higher FPR may be acceptable in exchange for higher sensitivity.
Is FPR the same as the Type I error rate?
Yes — in classical statistical hypothesis testing terms, FPR is exactly the Type I error rate (rejecting a true null hypothesis, or here, flagging a true negative as positive).