Cosine similarity

Cosine similarity compares the direction of two vectors by dividing their dot product by their lengths.

cosine(a, b) = (a · b) / (length(a) × length(b))

Tiny example

[1, 0] and [0.9, 0.1] point in similar directions, so their cosine score is near 1. [1, 0] and [0, 1] are perpendicular and score 0.

What it does not mean

A score of 0.82 does not mean “82% relevant,” correct, or confident. It is a geometric score inside one embedding model’s space. Calibrate relevance thresholds on the chosen model and corpus.

See the worked code in vector search foundations.