Math

Cosine Similarity Calculator

Measure the cosine of the angle between two 3D vectors.

a₁

a₂

a₃

b₁

b₂

b₃

Calculated Output

Cosine similarity 0.9746

Angle (°) 12.933

Formula: cosθ = (a · b) ÷ (|a| |b|)

Step-by-Step Breakdown

1. Values used:

2. a₁ = 1

3. a₂ = 2

4. a₃ = 3

5. b₁ = 4

6. b₂ = 5

7. b₃ = 6

9. Cosine similarity = 0.9746

10. Angle = 12.933°

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The math behind it

Divide the dot product by the product of the magnitudes. The result ranges from −1 (opposite) through 0 (perpendicular) to 1 (identical direction).

(1,2,3) and (4,5,6) → cosine similarity ≈ 0.974 (about 13°).

Does magnitude matter?

No — cosine similarity ignores length and measures direction only.