What this calculator does
Youden J is sensitivity plus specificity minus one. A test that is 90% sensitive and 85% specific scores 0.75; one that is 50% on both scores exactly zero, which is the value for a test that performs no better than a coin flip.
The zero point is the useful feature. Adding the two rates and subtracting one puts chance performance at the origin, so the index measures how much better than guessing a test actually is. A test that is 99% sensitive but only 1% specific also scores zero, correctly, because it is simply calling everything positive.
The formula
The two rates are added and one is subtracted. The result runs from 0 for chance performance to 1 for a perfect test, and can in principle go negative for a test that performs worse than guessing. It weights sensitivity and specificity equally, which is its main limitation as well as its main simplification.
| Term | Meaning |
|---|---|
| Youden’s J | Sensitivity plus specificity minus 1. |
| Chance performance | Any test where sensitivity and specificity sum to 1, which scores zero. |
| ROC curve | The plot of sensitivity against 1 minus specificity across thresholds. J is the maximum vertical distance from the diagonal. |
| Optimal cutoff | The threshold maximising J is one common way to choose a cutoff. |
The inputs explained
| Field | What to enter |
|---|---|
| Sensitivity (%) (%) | Sensitivity as a percentage. |
| Specificity (%) (%) | Specificity as a percentage. |
When to use it
Comparing two tests
A single number allows a quick ranking where sensitivity and specificity point in different directions.
Choosing a cutoff
Maximising J across candidate thresholds is a standard method for selecting a diagnostic cutoff.
Summarising a ROC analysis
J corresponds to the greatest vertical distance between the ROC curve and the chance diagonal.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What does each combination score?
A range of test performances.
| Sensitivity (specificity 85%) | Youden's index (J) | Sensitivity | Interpretation |
|---|---|---|---|
| 15% | 0 | 15.0% | No better than random guessing |
| 50% | 0.3500 | 50.0% | Moderate diagnostic performance |
| 70% | 0.5500 | 70.0% | Moderate diagnostic performance |
| 90% | 0.7500 | 90.0% | Strong diagnostic performance |
| 99% | 0.8400 | 99.0% | Strong diagnostic performance |
Questions
What is a good Youden index?
Higher is better, with 1 perfect and 0 no better than chance. Values above about 0.5 are often described as strong and below 0.3 as weak, but these are conventions. What counts as acceptable depends entirely on the consequences of each error in the setting.
Why can the index be zero for a very sensitive test?
Because a test that calls everything positive has 100% sensitivity and 0% specificity, summing to one and scoring zero. It correctly identifies every case and provides no information, which is exactly what the index is designed to reveal.
Does Youden J weight the two equally?
Yes, and that is its main limitation. It assumes a false negative and a false positive cost the same, which is rarely true in practice. Where one error is much worse, a weighted measure or an explicit cost analysis is more appropriate.
How is it used to pick a cutoff?
By calculating J at every candidate threshold and choosing the one that maximises it. This is a common default, though it inherits the equal-cost assumption. If false negatives are more costly, a threshold favouring sensitivity is the better choice.
For the full metric set from raw counts, see the diagnostic test metrics calculator. For specificity on its own, see the specificity calculator.