Embeddings
Cosine similarity calculator
Paste two vectors to calculate their cosine similarity, dot product, and Euclidean norms. The breakdown makes it clear whether a score changed because of direction or magnitude.
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1. Enter two equal-length vectors
Numbers separated by commas, spaces, or lines
Must have the same number of dimensions
Try an example:
Results update as you type.
Cosine similarity0
Directional alignment
Dot product0
Σ(Aᵢ × Bᵢ)
Norm A0
Length of vector A
Norm B0
Length of vector B
Formula
cosine similarity = dot(A, B) ÷ (||A|| × ||B||)
Cosine similarity is undefined for a zero vector. For embeddings, use the same model and preprocessing on both sides, then calibrate any threshold on your own labeled examples.
Read the full explanation
See cosine similarity explained with examples for the worked arithmetic, embedding-search guidance, and common mistakes.