📐 Cosine Similarity Calculator

Measure the cosine of the angle between two vectors in high-dimensional space.

Similarity Calculator

Enter vector components to calculate cosine similarity and distance.

Number of Dimensions

Vector A

Component 1

Component 2

Component 3

Vector B

Component 1

Component 2

Component 3

Cosine Similarity

0.0000

Cosine Distance

0.0000

Calculation Details:

Dot Product (A·B): 32.0000

Magnitude of A: 3.7417

Magnitude of B: 8.7750

Similarity = 32.0000 / (3.7417 × 8.7750) = 0.0000

About Cosine Similarity

Cosine similarity measures the cosine of the angle between two vectors, focusing on orientation rather than magnitude.

Formula:

cos(θ) = (A·B) / (||A|| × ||B||)

Range: -1 to 1
1: Identical direction
0: Orthogonal (90°)
-1: Opposite direction

Use Cases

• Document similarity in text mining
• Recommendation systems
• Image recognition and comparison
• Natural language processing
• Collaborative filtering
• Gene expression analysis

Key Insight: Cosine similarity is independent of vector magnitude, making it ideal for comparing documents of different lengths or feature vectors with different scales.