False Positive Rate

A key error metric for alarms and classifiers. Lower FPR means fewer false alarms among true negatives.

FPR % = false positives ÷ (false positives + true negatives) × 100.

Tip: Keep “False Positives (FP)” and “True Negatives (TN)” on the same basis (period, units, and population) before calculating False Positive Rate.

Cluster: Statistics hub · Percentage error · Percentage guide

False positive rate (FPR) is the share of actual negatives incorrectly flagged as positive.

Enter false positives (FP) and true negatives (TN).

Incorrect positive calls
Correct negative calls

False Positive Rate

Understanding False Positive Rate

How we calculate. FPR % = false positives ÷ (false positives + true negatives) × 100. The form uses the same arithmetic as the worked examples on this page. See our methodology and accuracy policy.

Real-world scenario: A typical False Positive Rate case uses false positives (fp) 40 and true negatives (tn) 960. Enter the same figures below to reproduce the worked path.

What is False Positive Rate?

A key error metric for alarms and classifiers. Lower FPR means fewer false alarms among true negatives.

  • Complement of specificity (when same counts)
  • Threshold-dependent
  • Cost of false alarms varies

The Formula

False Positive Rate
FPR % = FP ÷ (FP + TN) × 100

Worked Example

Scenario: FP = 40, TN = 960.
Step 1: 40 ÷ (40+960) = 0.04
Step 2: × 100 = 4%
Answer: False positive rate is 4%.

Common Use Cases

  • Security alerts: noise rate
  • Medical screens: false alarm share
  • ML ops: threshold tuning

Pro Tips

  • Balance with false negatives
  • Report base rates
  • Use precision when positives are rare

Limitations: False Positive Rate results are educational statistics aids—not formal statistical certification. Confirm assumptions (SRS, large-sample approximations, labeling) for your analysis.

FAQ

FPR vs FDR?

FPR is among actual negatives. False discovery rate is FP/(TP+FP) among predicted positives.

What if FP+TN is 0?

FPR is undefined—no actual negatives in the set.

Authoritative References

For statistical definitions and survey practice, consult:

  • NIST ITL — measurement and statistical guidance
  • AAPOR — survey response-rate standards
  • NCHS — public health statistics context