Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
Distance formulas
One dimension
The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates
Two dimensions
Higher dimensions
In three dimensions, for points given by their Cartesian coordinates, the distance is
Example: the distance between the two points (8,2,6) and (3,5,7):
In general, for points given by Cartesian coordinates in n-dimensional Euclidean space, the distance is