NDCG Calculator
Normalized Discounted Cumulative Gain — the gold-standard ranking metric with graded relevance and position discounting.
NDCG handles GRADED relevance (a perfect result beats a merely-okay one) and discounts by position via log₂, then normalizes so 1.0 is the best possible ordering. It's the default offline metric at every major search/recommendation company.
Formula
About NDCG Calculator
NDCG is the most complete ranking metric and the offline standard at search and recommendation companies, because it handles two things simpler metrics ignore: graded relevance (a perfect result should outrank a merely-acceptable one) and position discounting (relevance at rank 1 is worth more than at rank 10, via a log₂ discount). It then normalizes by the ideal ordering so scores land in [0,1] and compare across queries. This calculator computes DCG, the ideal DCG, and the normalized NDCG@K from your graded relevance list — the exact computation libraries run.
How to use NDCG Calculator
- 1Enter your values into NDCG Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
- 2The result recomputes live using the formula shown on the page; there is no button to press.
- 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.
Why use NDCG Calculator?
- ✓Computes NDCG instantly in your browser — no sign-up, no upload, no server round-trip.
- ✓100% free and unlimited, with the exact formula shown: DCG@K = Σ (2^relᵢ − 1) / log₂(i+1).
- ✓Runs entirely client-side, so every value you enter stays private on your device.
- ✓Live recompute as you type, with a worked example and authoritative references for trust.
Frequently asked questions
Why does NDCG use graded relevance instead of binary?+
Because real relevance isn't yes/no — a perfect match, a decent result and a tangential one are genuinely different, and a ranker that puts the perfect result first should beat one that leads with the decent one. The 2^rel − 1 gain term rewards surfacing the BEST items high, not just any relevant item.
What does the log₂ discount represent?+
User attention decay with position. Dividing each result's gain by log₂(position+1) means rank 1 keeps full value, rank 3 is worth ~0.63, rank 7 ~0.36 — modeling how dramatically click-through and attention drop down the list. It's an empirical choice that matches observed user behavior reasonably well.
Why normalize to get NDCG rather than just using DCG?+
Raw DCG depends on how many relevant items exist and their grades, so it's not comparable across queries — an easy query with many perfect results inflates DCG. Dividing by the ideal DCG (the best achievable ordering) rescales every query to [0,1], where 1.0 means 'perfectly ordered', making averaging across queries meaningful.
NDCG vs MAP — which to use?+
NDCG when relevance is graded (star ratings, 0–3 judgments) and position matters — the richer, more common choice for modern ranking. MAP when relevance is binary and you want a precision-recall-flavored summary. NDCG is generally preferred for learning-to-rank because it directly captures the graded, position-aware quality users experience.
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