Euclidean distance

(definition)

Definition: The straight line distance between two points. In a plane with p₁ at (x₁, y₁) and p₂ at (x₂, y₂), it is √((x₁ - x₂)² + (y₁ - y₂)²).

See also rectilinear, Manhattan distance, L_m distance.

Note: In N dimensions, the Euclidean distance between two points p and q is √(∑_i=1^N (p_i-q_i)²) where p_i (or q_i) is the coordinate of p (or q) in dimension i.

Author: PEB

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 17 December 2004.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "Euclidean distance", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/euclidndstnc.html