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The discounted cumulative gain (DCG) accumulated at a particular rank position <math>p</math> is defined as: <math> \mathrm{DCG_{p}} = rel_{1} + \sum_{i=2}^{p} \frac{rel_{i}}{\log_{2}i} </math> Normalized DCG (nDCG) is a way to calculate this measure across multiple queries, the results for which might all be of different length. nDCG is computed as: <math> \mathrm{nDCG_{p}} = \frac{DCG_{p}}{IDCG{p}} </math> The nDCG values for all queries can be averaged to obtain a measure of the average performance of a search engine's ranking algorithm.

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