Precision@$k$ (written P@$k$) is a top-$k$ ranking evaluation metric used in information retrieval. For a single query with a set $R$ of gold relevant items and a ranked list of retrieved items, let $R_k$ be the set of items appearing in the top $k$ positions. Then

$\mathrm{Precision@}k = \frac{|R \cap R_k|}{k}.$

The corpus-level score averages this quantity over a fixed evaluation set of queries. Precision@$k$ takes values in $[0,1]$ and is rank-agnostic within the top-$k$ window: it counts how many of the top $k$ retrieved items are relevant, not their internal ordering. The cutoff $k$ must be reported alongside the score (e.g. P@$10$), and meaningful headline comparisons fix the encoder, candidate pool, cutoff, matching rule, and split policy so that two systems compute denominators of the same size $k$ and a comparable numerator. Unlike Recall@$k$, the denominator is the fixed cutoff $k$ rather than $|R|$, so P@$k$ is sensitive to how many relevant items exist per query and is typically reported alongside Recall@$k$ as a complementary precision-side measure.