Youden Index Calculator (J = sensitivity + specificity − 1)

Understanding the Youden index calculator — concept and principle

This calculator computes Youden's index J for a diagnostic test or a test cut-off, from sensitivity and specificity or from the counts of a 2 × 2 table. It also gives J as a percentage, balanced accuracy and the positive and negative likelihood ratios. Use it for evaluating screening tests, choosing ROC cut-offs, and epidemiology and biostatistics courses.

Sensitivity comes from the disease column and specificity from the no-disease column; J adds them and subtracts 1.

How it is calculated

Sensitivity = TP ÷ (TP + FN); specificity = TN ÷ (TN + FP).
Youden's J = sensitivity + specificity − 1.
Balanced accuracy = (J + 1) ÷ 2 = (sensitivity + specificity) ÷ 2.
Positive likelihood ratio LR+ = sensitivity ÷ (1 − specificity).
Negative likelihood ratio LR− = (1 − sensitivity) ÷ specificity.

The principle

J measures how much better a test separates people with and without a condition than chance. A useless test that labels people positive at random has a true positive rate equal to its false positive rate, so sensitivity + specificity = 1 and J = 0. A perfect test has J = 1. On an ROC curve, which plots sensitivity against 1 − specificity, J is the vertical distance from the curve to the diagonal line of chance, so the cut-off with the largest J is a common choice when false positives and false negatives matter equally. J was proposed by W. J. Youden in 1950.

Worked example

Default inputs: counts TP = 85, FN = 15, TN = 160, FP = 40.

Sensitivity = 85 ÷ 100 = 85%.
Specificity = 160 ÷ 200 = 80%.
J = 0.85 + 0.80 − 1 = 0.65 (65%).
Balanced accuracy = (0.65 + 1) ÷ 2 = 82.5%.
LR+ = 0.85 ÷ 0.20 = 4.25; LR− = 0.15 ÷ 0.80 = 0.1875. Reading: better than chance.

Each point is the calculator re-run with only “True negatives TN (counts)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

True negatives TN (counts)	Youden index J
40	0.35
80	0.5167
120	0.6
160	0.65
200	0.6833
240	0.7071
320	0.7389

How to read the result

J ranges from −1 to 1. Values near 0 mean the test is no better than chance; values near 1 mean excellent separation. Negative values mean the labels are effectively reversed. LR+ above about 10 or LR− below about 0.1 are often described as strong evidence, but this is a rule of thumb. J ignores prevalence and treats both kinds of error as equally bad.

Common mistakes

Swapping FN and FP when entering the table.
Using J to choose a cut-off when one type of error is much more costly than the other.
Comparing J values from studies with very different populations.
Confusing sensitivity and specificity with predictive values, which depend on prevalence.

Keep in mind: This tool summarises test statistics; it is not a diagnosis. Test choice and interpretation belong to qualified clinicians and depend on the clinical setting and prevalence.

Frequently asked questions

What is a good Youden index?

There is no fixed threshold; higher is better, and the value should be compared with other tests or cut-offs in the same setting.

How is J related to the ROC curve?

J at a cut-off is the vertical distance from that point on the ROC curve to the diagonal.

Does J depend on how common the condition is?

No. Sensitivity and specificity, and therefore J, do not depend on prevalence.

Sources: Youden, W. J. (1950), "Index for rating diagnostic tests", Cancer 3(1), 32–35 · Fluss, Faraggi & Reiser (2005), Biometrical Journal 47(4), 458–472

Checked 9 Nov 2026. Youden’s J = sensitivity + specificity − 1 (standard definition, Youden 1950); use as a summary of the ROC curve and for choosing a cut-off as described by Fluss, Faraggi & Reiser (2005), “Estimation of the Youden Index and its associated cutoff point”, Biometrical Journal 47(4), 458–472. Likelihood ratios: standard formulas.

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