How to Use the Vector Similarity & Cosine Distance Calculator
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Enter two numerical vectors of identical dimension into Vector A and Vector B.
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Check or uncheck L2 Unit Normalization (recommended for modern vector databases).
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Instantly view Cosine Similarity, Cosine Distance, Euclidean L2 Distance, and Dot Product.
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Review the semantic similarity tier assessment for vector retrieval applications.
Practical Example & Use Case
Calculating cosine similarity (0.9982) between two document embedding vectors to determine if they meet the similarity threshold for a deduplication pipeline.
Technical Notes & Limitations
Supports multi-dimensional vectors (from 2D coordinates up to 1536-dimension OpenAI text-embedding-3 vectors). Dimensionality of Vector A and Vector B must match.
Frequently Asked Questions
What is the relationship between Cosine Similarity and Cosine Distance?
Cosine Distance is defined as `1 - Cosine Similarity`. When two vectors point in the identical direction, similarity is 1.0 and distance is 0.0.
Why do vector databases normalize embeddings to unit length?
When vectors are L2-normalized (length = 1.0), Cosine Similarity is mathematically identical to Dot Product, enabling ultra-fast hardware-accelerated matrix multiplication.
What does an orthogonal vector similarity score mean?
A cosine similarity near 0.0 means the two vectors are orthogonal (at a 90° angle), indicating zero semantic correlation between the corresponding concepts.