What does cosine similarity measure?

It measures the angle between two vectors, ignoring their magnitude. Values range from -1 (opposite direction) through 0 (orthogonal, unrelated) to 1 (identical direction). For text embeddings it is the standard measure of semantic similarity.

Why does it ignore magnitude?

Many embedding models encode meaning in direction rather than length. Cosine similarity normalises out the magnitude so two vectors pointing the same way score 1 even if one is longer, which is usually what you want for semantic comparison.

What if the vectors are different lengths?

Cosine similarity is only defined for vectors of equal dimension. The tool will tell you if the lengths differ so you can fix the input rather than getting a misleading number.

Is my data processed locally?

Yes. The calculation runs in your browser with no network calls, so embeddings you paste are never uploaded or stored.

Cosine Similarity Calculator

Cosine similarity calculator

Cosine similarity is the workhorse metric for comparing embeddings. Whether you are debugging a semantic search index, evaluating a RAG retriever, or checking whether two pieces of text are near-duplicates, you reduce it to: how aligned are these two vectors? This tool computes that alignment along with the underlying dot product and norms, so you can sanity-check a result without writing code.

How it works

Cosine similarity is the dot product of the two vectors divided by the product of their L2 norms:

cos(θ) = (A · B) / (‖A‖ × ‖B‖)

The tool parses both inputs into number arrays, verifies they have the same dimension, then computes the dot product (sum of element-wise products) and each vector’s L2 norm (the square root of the sum of squares). Dividing gives a value in the range −1 to 1. A small interpretation note translates that number into plain language — near 1 means very similar, near 0 means unrelated, negative means opposed.

Tips and notes

Both inputs must match in length. A 1536-dim OpenAI embedding only compares to another 1536-dim vector.
Cosine vs distance. Cosine distance is simply 1 − similarity; some vector databases report distance, so a “0.1 distance” means 0.9 similarity.
Pre-normalised vectors. If your embeddings are already unit length, the cosine similarity equals the dot product — a handy cross-check.
Local only. Vectors are processed entirely in your browser.