What is Euclidean distance in vector retrieval?

Euclidean distance measures the straight-line distance between two vectors in embedding space.

In vector retrieval, a smaller Euclidean distance means the query embedding and document embedding are closer together.

How it works

Suppose:

Query = [1, 2]

Document = [4, 6]

Euclidean distance is:

sqrt((4 - 1)^2 + (6 - 2)^2)

= sqrt(9 + 16)

= 5

The smaller this distance, the more similar the vectors are considered.

How retrieval uses it

During RAG retrieval:

User query → convert to embedding → compare with document embeddings → calculate distances → rank documents from smallest distance to largest

So unlike cosine similarity or dot product, where a larger score usually means a stronger match, Euclidean distance works in the opposite direction:

Smaller distance → more similar

Larger distance → less similar

Why vector magnitude matters

Euclidean distance considers the actual positions of vectors, including their magnitude.

For example:

A = [1, 1]

B = [2, 2]

Even though A and B point in the same direction, they are not at the same location.

Their Euclidean distance is greater than zero.

Cosine similarity, however, would treat them as having the same direction and give a cosine similarity of 1.

This is one of the main differences between the two metrics.

What happens with normalized embeddings?

If embeddings are normalized so every vector has unit length, Euclidean distance and cosine similarity become closely related.

For unit-normalized vectors:

smaller Euclidean distance ↔ higher cosine similarity

This means they usually produce the same ranking.

So when embeddings are normalized, choosing between cosine similarity and Euclidean distance may make little difference to retrieval order.

When should Euclidean distance be used?

Use it when:

• The embedding model is designed for Euclidean distance
• Absolute position and magnitude in embedding space are meaningful
• The model provider recommends L2 or Euclidean distance

Do not choose the metric only because it sounds intuitive.

The distance function should match how the embedding model was trained.

Euclidean distance vs cosine similarity

Cosine similarity asks:

"How similar are the directions of these vectors?"

Euclidean distance asks:

"How far apart are these vectors in space?"

That distinction matters when vectors have different magnitudes.

Interview takeaway

Euclidean distance measures the straight-line distance between two embeddings. Smaller distance means greater similarity. Unlike cosine similarity, Euclidean distance is affected by both direction and magnitude. If embeddings are unit-normalized, Euclidean distance and cosine similarity usually produce equivalent rankings. The best metric depends on how the embedding model was trained.