Euclidean Distance Calculator
Calculate the Euclidean (L2) distance between two vectors in n-dimensional space.
Inputs
Comma-separated values
Comma-separated values
Euclidean Distance
5.196152
Dimensions
3
Step by step
Sum of squared differences
Σ(aᵢ − bᵢ)²
= 27.0000
Euclidean distance: √(sum)
√27.0000
= 5.196152
How it works
Euclidean distance is the straight-line distance between two points in n-dimensional space, computed as the square root of the sum of squared differences across each dimension. It is the most common distance metric used in k-nearest neighbors, clustering algorithms, and vector similarity searches.
Formula
Euclidean Distance
d(a, b) = sqrt(sum((a_i - b_i)^2))
- a, b
- Input vectors
Frequently Asked Questions
When should I use Euclidean distance vs cosine similarity?
Use Euclidean distance when the magnitude of vectors matters (e.g., physical distance, raw feature values). Use cosine similarity when only the direction matters (e.g., text embeddings, TF-IDF vectors).
Does Euclidean distance work well in high dimensions?
In very high dimensions, distances between points tend to converge (curse of dimensionality), making Euclidean distance less discriminative. Dimensionality reduction or alternative metrics may help.