Euclidean distance

conventional distance in mathematics and physics

In Euclidean geometry, the Euclidean distance is the usual distance between two points p and q. This distance is measured as a line segment. The Pythagorean theorem can be used to calculate this distance.[1][2]

Euclidean distance on the planeEdit

Euclidean distance in R2

In the Euclidean plane, if p = (p1p2) and q = (q1q2) then the distance is given by[3]


This is equivalent to the Pythagorean theorem, where legs are differences between respective coordinates of the points, and hypotenuse is the distance.

Alternatively, if the polar coordinates of the point p are (r1, θ1) and those of q are (r2, θ2), then the distance between the points is


Related pagesEdit


  1. Weisstein, Eric W. "Distance". Retrieved 2020-09-01.
  2. "Distance Between 2 Points". Retrieved 2020-09-01.
  3. "Distance Between 2 Points". Retrieved 2020-09-01.