Calculator inputs
Formula used
False Positive Rate = False Positives ÷ (False Positives + True Negatives)
Specificity equals TN ÷ (TN + FP), so FPR also equals 1 − specificity.
How to use this calculator
- Choose full matrix, direct counts, or specificity conversion.
- Enter non-negative confusion-matrix counts.
- Add cost, target, threshold, and precision settings.
- Optionally paste multiclass, threshold, or prediction CSV data.
- Select Calculate to review metrics, charts, intervals, and exports.
Example data
| Input | Value | Meaning |
|---|---|---|
| False positives | 20 | Actual negatives incorrectly predicted positive. |
| True negatives | 180 | Actual negatives correctly predicted negative. |
| FPR | 10% | Twenty errors among two hundred actual negatives. |
Understanding false positive rate
False positive rate measures errors among actual negative cases. It is not the percentage of positive predictions that are wrong. That second measure is the false discovery rate.
Thresholds often create a trade-off between false alarms and missed positives. Raising a threshold commonly lowers FPR but can reduce recall. Select thresholds using operational costs and safety requirements.
For multiclass classification, each class can be evaluated against all other classes. Micro averaging combines counts before calculating FPR. Macro averaging treats every class equally.
Frequently asked questions
What is a good false positive rate?
There is no universal target. The acceptable rate depends on false-alarm costs, recall requirements, prevalence, regulation, and the deployment environment.
Is false positive rate the same as false discovery rate?
No. FPR uses all actual negatives as its denominator. False discovery rate uses all predicted positives as its denominator.
How is FPR related to specificity?
They are complements. FPR equals one minus specificity, while specificity equals one minus FPR.
Can FPR be calculated without true negatives?
Not from false positives alone. You need the number of actual negatives, true negatives, or an already calculated specificity value.
Why can accuracy look high when FPR is poor?
Accuracy mixes every class and error type. Class imbalance can hide a harmful false-positive pattern inside a strong overall accuracy.
What happens when FP plus TN equals zero?
The dataset contains no actual negatives. FPR is undefined because its denominator is zero.
Should weighted counts be integers?
No. Sample weighting can produce decimals. This calculator accepts non-negative weighted counts and calculates proportional metrics normally.
How should multiclass FPR be reported?
Report per-class one-vs-rest rates and clearly name the averaging method. Macro, micro, and weighted averages answer different questions.
Does the lowest FPR threshold always win?
No. A very high threshold can lower false alarms while missing important positives. Compare FPR with recall, precision, and practical costs.
What does the confidence interval show?
It shows plausible uncertainty around the observed FPR under a binomial sampling model. Larger negative-class samples usually produce narrower intervals.
Can this calculator create an ROC curve?
Yes. Provide confusion matrices across thresholds or raw labels and scores. The chart plots true positive rate against false positive rate.
Locally saved calculations
Saved only in this browser. No calculations are sent elsewhere by this feature.