Youden's J Index (Youden Index) Calculator

Youden's J index (also called the Youden index or J statistic) was introduced by W. J. Youden in 1950 as a way to rate diagnostic tests with one number. It combines the two error-free rates of a binary test — how many true positives it catches and how many true negatives it catches — into a single value on a −1 to +1 scale.

The calculation has two equivalent paths, and this tool runs both:

1. From a confusion matrix, first derive the two rates. Sensitivity (the true positive rate) is Se = TP / (TP + FN) and specificity (the true negative rate) is Sp = TN / (TN + FP). These are the standard scikit-learn definitions.
2. From rates entered directly, use the given sensitivity and specificity as-is (a percentage is divided by 100).
3. Apply the classical definition: J = Se + Sp − 1.
4. Cross-check with the ROC identity J = TPR − FPR, where the false positive rate is FPR = 1 − Sp. On an ROC plot this is the vertical gap between the operating point and the chance diagonal — the quantity Fluss et al. (2005) maximise to locate the optimal cut-point. The two forms are algebraically identical; the tool asserts they agree before showing a result.

Interpretation follows a common rule of thumb — J below 0.2 is poor, 0.2–0.4 fair, 0.4–0.6 moderate, 0.6–0.8 good, and above 0.8 excellent — with J = 0 flagged as no better than chance and a negative J flagged as probably-inverted labels. These bands are a guide, not an official standard: J is best read relative to your base rates and the real cost of a false positive versus a false negative. If either the positive class (TP + FN) or the negative class (TN + FP) is empty, sensitivity or specificity is undefined, so the tool returns a specific message instead of a misleading zero. All arithmetic is exact and client-side, with rounding applied only for the four-decimal display.

• Youden, W. J. (1950) — “Index for rating diagnostic tests,” Cancer 3(1):32–35 (original J = Se + Sp − 1)
• Fluss, Faraggi & Reiser (2005) — “Estimation of the Youden Index and its associated cutoff point,” Biometrical Journal 47(4):458–472 (J as the ROC cut-point criterion)
• scikit-learn — model evaluation: sensitivity/recall (TPR) and specificity (TNR) definitions

The formulas and worked examples on this page were last cross-checked against these sources on 2026-07-13. Youden's J index is a long-established, stable definition; this page is reviewed if the cited references or the scikit-learn metric conventions change.