Sensitivity, Specificity, PPV & NPV Calculator: Diagnostic Accuracy Guide:
Understanding Diagnostic Test Metrics:
These statistical measures evaluate a test’s ability to:
- Sensitivity: Detect true positives (avoid missed cases)
- Specificity: Identify true negatives (avoid false alarms)
- PPV: Confirm disease when test is positive
- NPV: Rule out disease when test is negative
Formulas Based on 2×2 Contingency Table
| Disease (+) (Gold Standard) | Disease (-) (Gold Standard) | |
|---|---|---|
| Test (+) | True Positive (TP) | False Positive (FP) |
| Test (-) | False Negative (FN) | True Negative (TN) |
Sensitivity =
TP
TP + FN
× 100%
Specificity =
TN
TN + FP
× 100%
PPV =
TP
TP + FP
× 100%
NPV =
TN
TN + FN
× 100%
Accuracy =
TP + TN
TP + TN + FP + FN
× 100%
Key Definitions:
• TP: True Positive
• TN: True Negative
• FP: False Positive
• FN: False Negative
• Prevalence: (TP + FN) / Total
• TN: True Negative
• FP: False Positive
• FN: False Negative
• Prevalence: (TP + FN) / Total
Clinical Interpretation:
• Sensitivity: Rule-out value (SnNout)
• Specificity: Rule-in value (SpPin)
• PPV: Probability disease when test +
• NPV: Probability no disease when test –
• Accuracy: Overall correctness
• Specificity: Rule-in value (SpPin)
• PPV: Probability disease when test +
• NPV: Probability no disease when test –
• Accuracy: Overall correctness
Calculation Example:
COVID Test (n=1000): TP=90, TN=850, FP=50, FN=10
• Sensitivity = 90/(90+10) = 90%
• Specificity = 850/(850+50) = 94.4%
• PPV = 90/(90+50) = 64.3%
• NPV = 850/(850+10) = 98.8%
• Accuracy = (90+850)/1000 = 94%
• Sensitivity = 90/(90+10) = 90%
• Specificity = 850/(850+50) = 94.4%
• PPV = 90/(90+50) = 64.3%
• NPV = 850/(850+10) = 98.8%
• Accuracy = (90+850)/1000 = 94%
Performance Targets:
• Screening tests: High sensitivity (>95%)
• Confirmatory tests: High specificity (>90%)
• Diagnostic tests: Balance (80-90%)
• Critical tests: Both >95%
• PPV/NPV depend on prevalence
• Confirmatory tests: High specificity (>90%)
• Diagnostic tests: Balance (80-90%)
• Critical tests: Both >95%
• PPV/NPV depend on prevalence
Prevalence Impact:
• PPV increases with higher prevalence
• NPV decreases with higher prevalence
• Example: Same test (90% sens, 95% spec)
– 1% prevalence: PPV = 15.4%
– 20% prevalence: PPV = 81.8%
• NPV decreases with higher prevalence
• Example: Same test (90% sens, 95% spec)
– 1% prevalence: PPV = 15.4%
– 20% prevalence: PPV = 81.8%
Clinical Rules:
• SnNout: High Sens test negative → rules OUT disease
• SpPin: High Spec test positive → rules IN disease
• Likelihood Ratio + = Sens / (1 – Spec)
• Likelihood Ratio – = (1 – Sens) / Spec
• F1 Score = 2 × (PPV × Sens) / (PPV + Sens)
• SpPin: High Spec test positive → rules IN disease
• Likelihood Ratio + = Sens / (1 – Spec)
• Likelihood Ratio – = (1 – Sens) / Spec
• F1 Score = 2 × (PPV × Sens) / (PPV + Sens)
Common Test Profiles:
• D-dimer: High sens (97%), low spec (40%)
• Troponin: High spec (95%), mod sens (80%)
• PSA screening: Mod sens (70%), mod spec (90%)
• HIV ELISA: Both >99.5%
• Rapid strep: High sens (95%), mod spec (85%)
• Troponin: High spec (95%), mod sens (80%)
• PSA screening: Mod sens (70%), mod spec (90%)
• HIV ELISA: Both >99.5%
• Rapid strep: High sens (95%), mod spec (85%)
Limitations:
• Spectrum bias (tested population ≠ target)
• Verification bias (only positives verified)
• Inter-observer variability
• Threshold effect (cutoff selection)
• Prevalence affects PPV/NPV
• Accuracy misleading for imbalanced data
• Verification bias (only positives verified)
• Inter-observer variability
• Threshold effect (cutoff selection)
• Prevalence affects PPV/NPV
• Accuracy misleading for imbalanced data
Key Formulas Reference:
• Sensitivity = TP / (TP + FN) × 100% | Misses: FN
• Specificity = TN / (TN + FP) × 100% | False Alarms: FP
• PPV = TP / (TP + FP) | Depends on prevalence
• NPV = TN / (TN + FN) | Depends on prevalence
• Accuracy = (TP + TN) / Total × 100%
• Prevalence = (TP + FN) / Total × 100%
• F1 Score = 2 × (Precision × Recall) / (Precision + Recall) | (Recall = Sensitivity)
• Sensitivity = TP / (TP + FN) × 100% | Misses: FN
• Specificity = TN / (TN + FP) × 100% | False Alarms: FP
• PPV = TP / (TP + FP) | Depends on prevalence
• NPV = TN / (TN + FN) | Depends on prevalence
• Accuracy = (TP + TN) / Total × 100%
• Prevalence = (TP + FN) / Total × 100%
• F1 Score = 2 × (Precision × Recall) / (Precision + Recall) | (Recall = Sensitivity)
📊 Sensitivity, Specificity, PPV, NPV & Accuracy Calculator
📐 Formulas:
Sensitivity =
TP
TP + FN
× 100%
Specificity =
TN
TN + FP
× 100%
PPV =
TP
TP + FP
× 100%
NPV =
TN
TN + FN
× 100%
Accuracy =
TP + TN
TP + TN + FP + FN
× 100%
🖊️ Enter the Values:
Step-by-Step Calculation:
Scenario: New COVID-19 rapid test (n=500 patients)
- TP: 85
- FP: 15
- FN: 25
- TN: 375
- Sensitivity:
85 / (85 + 25) = 85/110 = 0.773 → 77.3%
Interpretation: Misses 22.7% of true cases - Specificity:
375 / (375 + 15) = 375/390 = 0.962 → 96.2%
Interpretation: 3.8% false positive rate - PPV:
85 / (85 + 15) = 85/100 = 0.85 → 85%
Interpretation: 85% chance of actual infection if test positive - NPV:
375 / (375 + 25) = 375/400 = 0.938 → 93.8%
Interpretation: 93.8% chance of no infection if test negative
Clinical Interpretation Guide
| Metric | Ideal Value | High Impact Use Cases |
|---|---|---|
| Sensitivity | >90% | Rule OUT disease (e.g., D-dimer for PE) |
| Specificity | >95% | Rule IN disease (e.g., biopsy for cancer) |
| PPV | >85% | Confirm diagnosis after positive screening |
| NPV | >90% | Exclude disease in low-risk patients |
Prevalence Matters!:
Prevalence dramatically affects PPV/NPV:
PPV (Bayesian Formula) =
Sensitivity × Prevalence
Sensitivity × Prevalence + (1 – Specificity) × (1 – Prevalence)
× 100%
Example:
Same test (77.3% sens, 96.2% spec):
- 5% Prevalence: PPV = 51.2%
- 20% Prevalence: PPV = 83.1%
Calculator Workflow
- Input:
- TP, FP, FN, TN values
- Prevalence (optional for PPV/NPV adjustment)
- Output:
- Sensitivity, Specificity, PPV, NPV with 95% CI
- Likelihood Ratios (LR+/LR-)
- F1 Score (harmonic mean of PPV/sensitivity)
Common Applications
- Test Validation:
Compare new rapid tests against gold standards - Clinical Decision Rules:
Validate PERC rule for PE exclusion - Screening Programs:
Optimize mammography/colonoscopy thresholds - Antimicrobial Stewardship:
Evaluate rapid AST assays
Limitations & Best Practices:
⚠️ Avoid These Errors:
- Ignoring spectrum bias (test performance varies by disease stage)
- Using tests in populations with mismatched prevalence
- Overlooking confidence intervals
✅ Best Practices:
- Calculate 95% Confidence Intervals for all metrics
- Report Likelihood Ratios (LR+ >10 = strong rule-in)
- Use Fagan’s Nomogram for post-test probabilities
Why These Metrics Matter
“PPV/NPV optimization reduces unnecessary biopsies by 38% and false diagnoses by 29%.”
– JAMA Internal Medicine (2023)
Specialty Applications:
- Oncology (biomarker validation)
- Infectious Diseases (rapid test evaluation)
- Cardiology (stress test interpretation)
Access Calculator:
Enter TP/FP/FN/TN → Get instant metrics + interpretation
✅ Key Advantages:
- Prevalence-adjusted PPV/NPV
- 95% CI calculations
- Exportable reports for research
- Built-in Fagan’s Nomogram
Disclaimer:
- Gold standard quality affects all metrics
- Always correlate with clinical context
- Follow STARD guidelines for test reporting
⚠️ Disclaimer:
The content on LabTestsGuide.com is for informational and educational purposes only. We do not guarantee the accuracy, completeness, or timeliness of the information provided. Always consult qualified healthcare professionals for medical advice, diagnosis, or treatment. LabTestsGuide.com is not liable for any decisions made based on the information on this site.
