What is mean reciprocal rank (MRR) and how is it calculated?

MRR scores a ranked system by where the first relevant result lands. For each query take the reciprocal of that rank, 1/1, 1/2, 1/3, …, and a query with no relevant result scores 0. MRR is the average of those reciprocal ranks across all queries, a value from 0 to 1 where higher is better.

What is the difference between MRR and MAP?

MRR only looks at the first relevant result per query, so it suits tasks with one right answer, question answering, known-item search. MAP (mean average precision) averages precision over every relevant result, rewarding systems that surface all of them. Use MRR when finding one good answer fast matters; use MAP when full recall across many relevant items matters.

What is the difference between MRR and NDCG?

MRR uses binary relevance and stops at the first hit, so it ignores everything below it. NDCG uses graded relevance (a result can be a 3, not just relevant/not) and a log position discount across the whole list, normalised by the ideal order. MRR is simpler and answer-focused; NDCG captures ranking quality with grades. We have a separate NDCG calculator if you need grades.

What is a good MRR score?

There is no universal threshold, a good MRR depends on the task and how hard the queries are. An MRR of 1.0 means every first relevant result sat at rank 1; 0.5 means first hits average around rank 2. The reliable reading is the lift over your own baseline on the same test set, not an absolute number copied from a different benchmark.

How do you handle a query with no relevant result in MRR?

By the TREC QA convention (Voorhees, 1999) a query with no relevant result in the returned list gets a reciprocal rank of 0, and it still counts toward Q, the number of queries. So three queries scoring 1, 0.2 and 0 give MRR = 1.2 / 3 = 0.4. In this tool, enter 0 or “none” in ranks mode, or an all-zero line in list mode.

Do the two input modes give the same MRR?

Yes. A relevance list is just a longer way of stating the first-hit rank: 0, 0, 1 means the first relevant result is at rank 3, exactly like typing 3. So ranks “3, 1, 5” and the lists 0,0,1 / 1 / 0,0,0,0,1 both give MRR = 0.5111. List mode is handy when you already have 0/1 judgements; ranks mode is faster when you only noted the position.

What is the range of MRR, and what does rank 1 contribute?

MRR is always between 0 and 1. The first position contributes 1/1 = 1, rank 2 contributes 0.5, rank 3 about 0.333, and so on, the penalty for being lower drops off quickly. Because only the first relevant result counts, moving it from rank 2 to rank 1 raises MRR far more than reshuffling results further down.

Is my data sent anywhere?

No. The whole calculation runs in your browser with JavaScript, no upload, no API call, no account. You can paste evaluation data from an internal RAG or search system safely, and the page works offline once loaded.

AI · Machine learning

Mean Reciprocal Rank (MRR) Calculator

Paste the first-hit rank of each query, or a 0/1 relevance list per query, and get MRR with every reciprocal rank and the full arithmetic shown. The standard information-retrieval / TREC definition. No signup, nothing uploaded.

By Induwara Ashinsana· Co-Founder, Ryzera TechnologiesUpdated Jun 10, 2026

Mean Reciprocal Rank calculator

Input mode

First-hit rank per querye.g. 3, 2, 1Ranked relevance lists (0/1)one query per line

First-hit ranks (one value per query)

The rank (1, 2, 3, …) at which the first relevant result appeared for each query. Separate with commas, spaces or new lines. Use 0 or none for a query with no relevant result.

Round to

Examples

MRR

0.6111

0 to 1 · higher is better

Σ reciprocal ranks

1.8333

sum of 1/rankᵢ

Q (queries)

all returned a relevant result

Reading

Good ranking

MRR61.11% of the maximum

The arithmetic

MRR = (1/Q) · Σ (1/rankᵢ)

= (1/3) · (1/3 + 1/2 + 1/1)

= 1.8333 / 3

MRR = 0.6111

Cross-check. Summing the reciprocal ranks in input order gives 0.6111; an independent pass that sums them smallest-first gives 0.6111. They reconcile, as they must.

Per-query working

Query	First-hit rank	RRᵢ = 1/rank
#1	3	0.3333
#2	2	0.5000
#3	1	1.0000
Σ reciprocal ranks		1.8333

Method: MRR = (1/Q) · Σ 1/rankᵢ, where rankᵢ is the position of the first relevant result for query i and a no-hit query scores 0, the standard information-retrieval / TREC QA definition (Voorhees 1999; Manning et al., §8). Nothing leaves this page.

How it works

Mean Reciprocal Rank (MRR) measures how high up a ranked list the first relevant result appears, averaged over a set of queries. It is the headline metric for tasks that have one correct answer to find quickly, question answering, known-item search, entity lookup, and the retrieval step of a RAG pipeline. The definition here follows Voorhees (1999), who introduced MRR as the official score of the TREC-8 Question Answering track, and Manning, Raghavan & Schütze, §8.

Positions are 1-indexed. For each query i, let rankᵢ be the position of the first relevant result. The score is built in three steps:

Reciprocal rank. Take RRᵢ = 1 / rankᵢ. A first hit at rank 1 scores 1, rank 2 scores 0.5, rank 3 scores about 0.333, the reward drops off quickly as the first relevant result sinks lower.
No-hit convention. If a query returns no relevant result at all, RRᵢ = 0 (Voorhees, 1999). The query still counts toward Q, so misses pull the average down rather than being ignored.
Average. Add the reciprocal ranks and divide by the number of queries: MRR = (1/Q) · Σᵢ 1/rankᵢ, a value in [0, 1].

The two input modes are equivalent. In ranks mode you type the position directly. In relevance-list mode you give a 0/1 list per query and the tool finds the first 1 from the left, so 0, 0, 1 is read as rank 3, identical to typing 3; an all-zero line is a no-hit. Because MRR depends only on the first relevant position, anything below it is irrelevant to the score, that is exactly the difference from NDCG, which grades and discounts the whole list. As a credibility check, the calculator computes the average a second way, summing the reciprocal ranks smallest-first rather than in input order, and confirms the two routes agree to floating-point precision. Everything is deterministic and runs entirely in your browser.

Worked examples

Standard, first-hit ranks [3, 2, 1]

RR = 1/3, 1/2, 1/1 = 0.3333333, 0.5, 1
Σ RR = 1.8333333, Q = 3
MRR = 1.8333333 / 3 = 0.6111

With a miss, ranks [1, 5, none]

RR = 1/1, 1/5, 0 = 1, 0.2, 0 (the no-hit query scores 0)
Σ RR = 1.2, Q = 3 (the miss still counts toward Q)
MRR = 1.2 / 3 = 0.4000

List mode, [0,0,1,0] / [1,0,0] / [0,0,0,0,1]

first 1 at rank 3, 1, 5 ⇒ RR = 1/3, 1, 1/5
Σ RR = 1.5333333, Q = 3
MRR = 1.5333333 / 3 = 0.5111
Same as typing ranks 3, 1, 5, the modes agree.

Frequently asked questions

Sources & references

The formula on this page was last cross-checked against these sources on 2026-06-10. MRR is a stable mathematical definition, so this tool needs no rate or schedule updates, only the worked examples are periodically re-reconciled.

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