Vector Embedding Cosine Similarity Calculator

VECTOR EMBEDDING ARRAYS

Vector A (Comma or Space Separated Numbers)

0.12, 0.45, 0.88, 0.34, 0.91, 0.15, 0.62

Vector B (Comma or Space Separated Numbers)

0.15, 0.42, 0.85, 0.38, 0.89, 0.18, 0.59

SIMILARITY METRICS REPORT

Cosine Similarity Score

0.9984

Near Identical Directional Orientation

Dot Product (A · B): 1.9421

Euclidean Distance (L2): 0.0762

Vector Dimension Count: 7 Dimensions

Vector Embedding Cosine Similarity Guide

In Retrieval-Augmented Generation (RAG) and semantic search architectures, vector databases (Pinecone, Qdrant, pgvector) use cosine similarity to rank document relevance against user query embeddings.

Mathematical Formulation

Dot Product: Sum of element-wise products (A · B).
Cosine Similarity: Normalized dot product (A · B) / (||A|| * ||B||).
Metric Range: +1.0 (identical direction), 0.0 (orthogonal/unrelated), -1.0 (opposite direction).

Related AI Developer Tools

Audit vector retrieval with the RAG Retrieval Evaluator, calculate GPU memory needs with the GPU VRAM Calculator, or estimate BPE tokens with the LLM BPE Tokenizer.

Frequently Asked Questions

Common questions about this tool.

What is Cosine Similarity in AI & RAG systems? ▼

Cosine similarity measures the cosine of the angle between two multi-dimensional vector embeddings, producing a metric from -1.0 to +1.0 (where 1.0 indicates identical directional orientation).

What is the formula for Cosine Similarity? ▼

`Cosine Similarity = (A · B) / (||A|| * ||B||)` where `A · B` is the dot product and `||A||` is the L2 norm (magnitude) of vector A.

Why is Cosine Similarity preferred over Euclidean distance for text embeddings? ▼

Cosine similarity measures angle rather than magnitude, making it invariant to text length differences when comparing document embeddings.

What is normalized vector dot product? ▼

If vector embeddings are normalized to unit length (`||A|| = 1`), cosine similarity equals the dot product (`A · B`), reducing vector database query compute latency.

Is my vector embedding data kept private? ▼

100% private. All dot product and vector math operations run locally in JavaScript in your browser.