Precision@K and Recall@K Calculator

Precision@K and Recall@K evaluate the top K results a ranked system returns for a single query, a search engine, a recommender, or the retriever inside a RAG pipeline. Both start from the same count: how many of the top K results are actually relevant. Call that hits@K. These are the standard information-retrieval definitions from Manning, Raghavan & Schütze, Introduction to Information Retrieval (Chapter 8).

Precision@K asks how clean the top K is:Precision@K = hits@K / KOf the K results you showed, what fraction were right? It penalises padding the list with noise. Precision@K tends to fall as K grows, because you are forced to include lower-ranked, less certain results.

Recall@K asks how much of the relevant set you captured:Recall@K = hits@K / Rwhere R is the total number of relevant items that exist for the query. Recall@K rises (never falls) as K grows, because a deeper cutoff can only find more of the relevant set. If R = 0the ratio divides by zero, so recall is undefined and this tool reports N/A instead of a misleading 0.

F1@K combines the two into one number using the harmonic mean:F1@K = 2 · P · R / (P + R)The harmonic mean sits close to the smaller of the two, so a system cannot earn a high F1@K by being precise but incomplete, or thorough but noisy. There is an equivalent count form, F1@K = 2·hits / (K + R), that gives the same answer without ever forming precision or recall. This calculator computes F1@K both ways and cross-checks them, which is what the “Formulas verified” badge means.

Hit Rate@K is the simplest signal:Hit Rate@K = 1 if hits@K ≥ 1 else 0It answers “did we retrieve anycorrect result in the top K?”, the check RAG developers care about most, since one good chunk is often enough for the language model to answer. In ranked-list mode the tool recomputes all three ratio metrics at every cutoff from K = 1 to the list length, so you can watch the precision–recall trade-off and choose the top-K depth that fits your task.

• Manning, Raghavan & Schütze: Introduction to Information Retrieval, Ch. 8 (precision, recall, precision/recall at K)
• scikit-learn: Ranking metrics (top-K precision and recall)
• Wikipedia: Evaluation measures (information retrieval): precision@k, recall@k, F-measure

The definitions on this page were last cross-checked against the IR-book and scikit-learn on 2026-07-06. These are standard mathematical definitions that do not change over time; F1@K is verified by computing it two independent ways and confirming they agree.