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About this tool
Paste two embedding vectors and get cosine similarity, dot product, Euclidean distance and the angle between them.
This calculator computes the cosine similarity between two vectors — the dot product divided by the product of their L2 norms, giving a value between −1 and 1 that measures direction rather than magnitude. Alongside it you get the raw dot product, Euclidean (L2) and Manhattan (L1) distances, and the angle in degrees. It is built for developers working with text or image embeddings who want to sanity-check what their vector database is returning.
Open Cosine Similarity Calculator on AltFTool — it loads instantly in your browser.
Enter the values you already know.
Fine-tune the options to match your scenario.
Read the result and use it in your planning or reporting.
Cosine, dot product, Euclidean and Manhattan distance from a single paste — no notebook needed.
Accepts JSON arrays, comma-, space- or newline-separated numbers, up to 20,000 dimensions.
All arithmetic happens in your browser; embedding values are never uploaded anywhere.
Cosine similarity is the dot product of the two vectors divided by the product of their lengths: cos(θ) = (a·b) / (‖a‖ × ‖b‖). The result ranges from −1 (opposite directions) through 0 (orthogonal) to 1 (identical direction). Because it divides out magnitude, two vectors of very different lengths can still score 1 if they point the same way.
It depends on the model, but for modern text embeddings scores above roughly 0.8 usually indicate closely related content and above 0.95 near-duplicates. Scores are not comparable across models — a 0.7 from one embedding model can mean something different from a 0.7 from another, so always calibrate thresholds against your own data.
The dot product includes vector magnitude while cosine similarity normalises it away. If both vectors are unit-normalised (length 1), the two are exactly equal — which is why many vector databases store normalised embeddings and use the cheaper dot product internally. For unnormalised vectors, a long vector can win on dot product while pointing in a less similar direction.
Because the formula divides by the vector norms, and a zero vector has norm 0, making the division undefined. This calculator reports an error for an all-zeros vector instead of returning a misleading number. Euclidean and Manhattan distances remain well-defined and are still shown in that case only if both vectors parse.
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