NDCG Calculator
Calculate Normalized Discounted Cumulative Gain to evaluate ranking model quality.
About NDCG Calculator
NDCG measures ranking quality by comparing a predicted ranking's Discounted Cumulative Gain (DCG) against the ideal ranking (IDCG). DCG gives higher weight to relevant items appearing earlier in the ranking, using a logarithmic discount. NDCG = DCG / IDCG normalizes to [0, 1].
Formula
NDCG
NDCG = DCG / IDCG; DCG = sum((2^rel_i - 1) / log2(i + 2))
- rel_i
- Relevance score of item at position i
- IDCG
- DCG of the ideal (perfectly sorted) ranking
Worked example
With the default values below, NDCG Calculator returns NDCG of 0.9488. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Predicted Ranking Relevance
- 3, 2, 3, 0, 1, 2
- Ideal Ranking Relevance
- 3, 3, 2, 2, 1, 0
Results
- NDCG
- 0.9488
- DCG
- 13.8483
- IDCG
- 14.5954
Step by step
- 1DCG: Σ(2^rel_i − 1) / log₂(i+2)= 13.848264
- 2IDCG: same formula with ideal ordering= 14.595391
- 3NDCG = DCG / IDCG= 0.948811
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why use logarithmic discounting?
Users are much more likely to look at top-ranked results. The log discount reflects diminishing returns of later positions — a relevant result at position 1 is far more valuable than the same result at position 10.
When is NDCG preferred over precision@k?
NDCG is preferred when relevance is graded (not binary) and position matters. It captures both the relevance level and rank position, while precision@k only counts binary relevant/irrelevant.