What is the range of cosine similarity?

The score ranges from -1 to 1. A value of 1 indicates identical direction, 0 indicates orthogonality (no similarity), and -1 indicates completely opposite directions.

How do I enter vectors?

Enter comma-separated numbers, e.g. "1, 2, 3" or "0.5, -1.2, 4". Both vectors must have the same number of dimensions.

Does vector magnitude affect cosine similarity?

No. Cosine similarity is scale-invariant — multiplying all elements of a vector by a constant does not change its cosine similarity with another vector. Only direction matters.

What happens with a zero vector?

Cosine similarity is undefined when either vector is a zero vector (all elements are zero), because the magnitude would be zero and division by zero is not allowed. The tool will report this as an error.

How is this different from Euclidean distance?

Euclidean distance measures the straight-line distance between two points, so it is affected by magnitude. Cosine similarity only considers the angle between vectors, ignoring their length.

How do I calculate cosine similarity in Python?

Use scikit-learn: from sklearn.metrics.pairwise import cosine_similarity; cosine_similarity([a], [b]). Or compute it directly with NumPy: np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b)). This tool gives the same result without writing code.

Cosine Similarity Calculator

Enter two numeric vectors and instantly get their cosine similarity score, dot product, and magnitudes.

Input Vectors

Vector A (comma-separated numbers)

Vector B (same number of dimensions)

Quick Examples

Enter two vectors and click Calculate

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Summary

Enter two numeric vectors and instantly get their cosine similarity score, dot product, and magnitudes.

How it works

Enter two numeric vectors of the same dimension as comma-separated numbers.
The tool computes the dot product A · B and each vector magnitude (Euclidean norm).
It divides the dot product by the product of the magnitudes to get the cosine of the angle.
The result is the similarity score from -1 to 1, plus the angle in degrees and radians.

Use cases

Measure document or text similarity in NLP and information retrieval.
Compare user preference vectors in recommendation systems.
Evaluate word embeddings and semantic similarity between sentences.
Assess feature vector similarity in machine learning models.
Verify cosine distance calculations in data science projects.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu