Sensitivity and Specificity Calculator

From a confusion matrix with True Positives (TP), False Positives (FP), False Negatives (FN), and True Negatives (TN):

Sensitivity (True Positive Rate / Recall):

$$\text{Sensitivity} = \frac{TP}{TP + FN}$$

The proportion of actual positives correctly identified.

Specificity (True Negative Rate):

$$\text{Specificity} = \frac{TN}{TN + FP}$$

The proportion of actual negatives correctly identified.

Positive Predictive Value (Precision):

$$PPV = \frac{TP}{TP + FP}$$

Negative Predictive Value:

$$NPV = \frac{TN}{TN + FN}$$

Accuracy:

$$\text{Accuracy} = \frac{TP + TN}{TP + FP + FN + TN}$$

Prevalence:

$$\text{Prevalence} = \frac{TP + FN}{\text{Total}}$$

F1 Score (harmonic mean of precision and recall):

$$F_1 = \frac{2 \times PPV \times \text{Sensitivity}}{PPV + \text{Sensitivity}}$$

High sensitivity means few false negatives — the test catches most positive cases. Critical for ruling out serious diseases (a negative result is reassuring).

High specificity means few false positives — the test rarely triggers false alarms. Critical for confirmation testing (a positive result is reliable).

PPV and NPV depend on prevalence. In low-prevalence settings, even high sensitivity and specificity can yield low PPV (the false positive paradox).

The F1 score balances precision and recall into a single metric, useful when classes are imbalanced. It ranges from 0 (worst) to 1 (perfect).