Euclidean distance


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, Lm distance.

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

Author: PEB

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Entry modified 17 December 2004.
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Cite this as:
Paul E. Black, "Euclidean distance", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: