Convert Gini to KS and AUC
For a score used in automated credit decisions, enter Gini, AUC or KS to see the other two under the binormal model. Compare the measures at once with a reference table.
At spread ratio 1.00, Gini 60.0% corresponds to AUC 0.800 and KS 44.8%. KS is 0.75 times Gini.
KS against Gini
The curve shows KS against Gini under the binormal model at your spread ratio. If the ratio differs from 1, the dashed curve shows a ratio of 1 and the dot marks your score.
Reference values
| Gini | AUC | KS | KS ÷ Gini |
|---|---|---|---|
| 20% | 0.600 | 14.2% | 0.71 |
| 30% | 0.650 | 21.5% | 0.72 |
| 40% | 0.700 | 28.9% | 0.72 |
| 50% | 0.750 | 36.7% | 0.73 |
| 60% | 0.800 | 44.8% | 0.75 |
| 70% | 0.850 | 53.6% | 0.77 |
| 80% | 0.900 | 63.5% | 0.79 |
| 90% | 0.950 | 75.5% | 0.84 |
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See the formulas
Bad scores follow a normal distribution with mean 0 and spread 1, and good scores follow one with mean d and spread s. AUC = Φ(d ÷ √(1 + s²)) Gini = 2 × AUC − 1 KS = max Φ(x) − Φ((x − d) ÷ s) (s = 1: KS = 2 × Φ(d ÷ 2) − 1) d = √(1 + s²) × Φ⁻¹(AUC)
There is no exact formula between Gini and KS. This is an approximation under the binormal model, and a real score with skewed or lumpy distributions can sit away from the curve.
Gini to KS conversion
Gini, AUC and KS express the same score ranking in different units. This calculator converts between them under the binormal model using the measure you enter and the spread ratio.
For a lender, the cut-off and policy built on a score shape the credit decision. Use the converted measures to compare scores, then test the scorecard’s cut-off and policy on past applications.
Common questions
How do I convert Gini to KS?
Enter Gini and set the spread ratio. The calculator estimates KS under the binormal model because Gini and KS have no exact conversion for every score.
What is the relationship between Gini, AUC and KS?
They measure the same score ranking in different units. The calculator estimates conversions between them under the binormal model using the spread ratio.
How do I convert AUC to Gini?
Under the binormal model, Gini is twice AUC minus one. The calculator also uses the spread ratio to work out KS.
Is there an exact formula between Gini and KS?
No. Both measures depend on the shape of the score distributions, so a real score with skewed or lumpy distributions can sit away from the binormal curve.
How do I compare a vendor score’s KS with an in-house Gini?
Enter the vendor score’s KS and set the spread ratio. The calculator estimates its Gini under the binormal model, so you can compare the measures on the same ranking.