Manhattan distance

The Manhattan distance, also known as the L₁-distance is the distance between two points measured along axes at right angles. In a plane with p₁ at (x₁, y₁) and p₂ at (x₂, y₂), the Manhattan distance is:

, when m = 1.

It is so named because it is the distance a car would drive in a city laid out in square blocks, like Manhattan (neglecting that in Manhattan there are one-way streets and some oblique streets).

L₂-distance is called Euclidean distance.