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Euclidean metric


In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. With this distance, Euclidean space becomes a metric space. The associated norm is called the Euclidean norm. Older literature refers to the metric as Pythagorean metric. A generalized term for the Euclidean norm is the L2 norm or L2 distance.

The Euclidean distance between points p and q is the length of the line segment connecting them ().

In Cartesian coordinates, if p = (p1p2,..., pn) and q = (q1q2,..., qn) are two points in Euclidean n-space, then the distance (d) from p to q, or from q to p is given by the Pythagorean formula:


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