Sensitivity Calculator — True Positive Rate
Calculate the sensitivity (also called recall or true positive rate) of a diagnostic test or classifier. Enter the number of true positives and false negatives to see what proportion of actual positive cases were correctly detected.
Proportion of actual positives correctly identified
- 1
Total actual positives (TP + FN)
90 + 10 = 100 - 2
Sensitivity = TP ÷ (TP + FN)
90 ÷ 100 = 90Proportion of actual positive cases correctly identified.
How does this calculator work?
Sensitivity = TP ÷ (TP + FN). It is the fraction of actual positives that a test correctly flags. Enter true positives and false negatives: for example, 90 TP and 10 FN gives 90% sensitivity (10% miss rate). Pair with specificity (TN ÷ (TN + FP)) for a complete evaluation.
Formula
How this is calculated
Sensitivity measures how well a test detects cases that are truly positive. It is defined as the proportion of actual positives that the test correctly identifies: Sensitivity = TP / (TP + FN), where TP is the number of true positives (correctly flagged) and FN is the number of false negatives (missed cases). A sensitivity of 1.0 (100%) means no positive case was missed; a lower value means some positives were incorrectly labeled negative.
The complementary metric is the false negative rate (FNR), also called the miss rate: FNR = 1 − Sensitivity = FN / (TP + FN). In medical screening, high sensitivity is critical when missing a disease is dangerous — for example, a cancer screening test should ideally have sensitivity close to 100%.
Sensitivity alone does not tell the full story. A test that calls everyone positive has sensitivity 1.0 but is useless. Pair it with specificity (TN / (TN + FP)) to evaluate both sides of the confusion matrix — use the sensitivity-and-specificity calculator for a complete picture.
Frequently asked questions
Sensitivity is the true positive rate: how well the test detects actual positives (TP / (TP + FN)). Specificity is the true negative rate: how well it rules out actual negatives (TN / (TN + FP)). High sensitivity minimises missed cases; high specificity minimises false alarms.
It depends on context. Medical screening tests (cancer, HIV) typically target ≥ 95% sensitivity to minimise missed diagnoses. Industrial defect detection or recall-focused classifiers also aim high. Trade-offs against specificity must be considered for the specific application.
Yes. Sensitivity, recall, and true positive rate (TPR) are all names for the same metric: TP / (TP + FN). The term "sensitivity" is common in medical diagnostics; "recall" is standard in machine learning.
Also known as
TG we-Calculate Editorial Team. (2026). Sensitivity Calculator — True Positive Rate [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sensitivity-calculator
TG we-Calculate Editorial Team. "Sensitivity Calculator — True Positive Rate." TG we-Calculate. 2026. https://we-calculate.com/calculator/sensitivity-calculator.
TG we-Calculate Editorial Team, "Sensitivity Calculator — True Positive Rate," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sensitivity-calculator
@misc{wecalculate_sensitivity_calculator, title = {Sensitivity Calculator — True Positive Rate}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sensitivity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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