---
title: "Vector similarity"
slug: "vector-similarity"
category: "glossary"
tags: ["glossary", "ai-agents", "embeddings", "vectors", "search", "rag"]
status: "stable"
last_updated: 2026-05-14
summary: "Vector similarity measures how close two embedding vectors are in high-dimensional space, used to rank documents by semantic relevance to a query."
related:
  [
    "[[glossary/embedding]]",
    "[[glossary/reranker]]",
    "[[ai-agents/embeddings]]",
    "[[ai-agents/rag-retrieval]]",
    "[[backend/chromadb]]",
    "[[glossary/retrieval-augmented-generation]]",
  ]
---

## Overview

This page is the atomic definition. Retrieval implementation lives at [[ai-agents/rag-retrieval]] and [[ai-agents/embeddings]].

## Definition

Vector similarity is a scalar measure of how close two [[glossary/embedding]] vectors are in the embedding space. The three most common metrics: cosine similarity measures the angle between vectors, returning 1.0 for identical direction and 0.0 for orthogonal; it is independent of vector magnitude and is preferred for text embeddings. Dot product is the unnormalized inner product; faster to compute but magnitude-sensitive. Euclidean distance (L2 norm) measures geometric distance; lower is more similar. Most embedding models are trained to maximize cosine similarity between semantically related texts. Vector databases (pgvector, Qdrant, ChromaDB, Pinecone) build approximate nearest-neighbor (ANN) indexes (HNSW, IVFFlat) that return the top-k most similar vectors in sub-linear time. Exact search is O(n) per query; HNSW reduces this to O(log n) at the cost of occasional missed results.

## When it applies

Use cosine similarity for text embedding search unless the embedding model documentation specifies a different metric. Use approximate search (HNSW) for collections over ~50k vectors. Use exact search for small collections where recall must be perfect.

## Example

```sql
-- pgvector cosine similarity search:
SELECT id, content, 1 - (embedding <=> $1) AS score
FROM documents
ORDER BY embedding <=> $1
LIMIT 10;
```

## Related concepts

- [[glossary/embedding]] - the vectors being compared.
- [[glossary/reranker]] - the second-stage model that improves on raw similarity rankings.
- [[ai-agents/embeddings]] - embedding model choice affects the quality of similarity scores.
- [[ai-agents/rag-retrieval]] - the retrieval pipeline that runs vector similarity search.
- [[backend/chromadb]] - a vector database that wraps similarity search.

## Citing this term

> See [[glossary/vector-similarity|Vector similarity]] (llmbestpractices.com/glossary/vector-similarity).

## Related

- [[glossary/embedding]]
- [[glossary/reranker]]
- [[ai-agents/embeddings]]
- [[ai-agents/rag-retrieval]]
- [[backend/chromadb]]