Enter the number of concordant pairs (C), discordant pairs (D), and the total number of comparable pairs (N) into the calculator to determine the Concordance Index (C-index). If N is greater than C + D, the remaining pairs are treated as ties (T = N − C − D) and counted as half credit in the C-index.

Concordance Index Calculator

Enter exactly 3 values to calculate the missing variable (ties are inferred as T = Total − Concordant − Discordant).

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Concordance Index Formula

The following formula is used to calculate the Concordance Index (C-index).

C-index = (C + 0.5T) / N
N = C + D + T

Variables:

  • C-index is the Concordance Index
  • C is the number of concordant pairs
  • D is the number of discordant pairs
  • N is the total number of comparable pairs; T is the number of tied pairs (so N = C + D + T)

To calculate the Concordance Index, count the number of concordant pairs (C) and discordant pairs (D) among the comparable pairs, and (if applicable) the number of tied pairs (T). Then compute C-index = (C + 0.5T)/N, where N = C + D + T. The C-index ranges from 0 to 1: 0.5 suggests performance no better than random ordering, 1.0 indicates perfect ranking, and values below 0.5 indicate worse-than-random (inversely ordered) predictions. For binary outcomes without censoring, the C-index is equivalent to the area under the ROC curve (AUC).

What is a Concordance Index?

A Concordance Index, also known as C-index, is a statistical measure used in predictive modeling to evaluate how well a model ranks outcomes. It is commonly used in survival analysis and compares the relative ranking of predicted risk to observed event times across comparable pairs. The C-index ranges from 0 to 1, where 0.5 indicates a model no better than random ordering and 1.0 indicates a perfect model. For binary outcomes without censoring, it is equivalent to the area under the receiver operating characteristic (ROC) curve (AUC).

How to Calculate Concordance Index?

The following steps outline how to calculate the Concordance Index.

  1. Determine the number of concordant pairs (C).
  2. Determine the number of discordant pairs (D).
  3. Determine the number of tied pairs (T), if applicable (pairs where the model gives tied/indistinguishable predictions).
  4. Calculate the total number of comparable pairs: N = C + D + T.
  5. Calculate the Concordance Index: C-index = (C + 0.5T) / N.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Number of concordant pairs (C) = 25

Number of discordant pairs (D) = 10

Total number of comparable pairs (N) = 50 (so tied pairs T = 50 − 25 − 10 = 15; C-index = (25 + 0.5×15) / 50 = 0.65)