Radial distance (geometry)

In geometry a radial distance, typically denoted r, is a coordinate in polar coordinate systems (r, θ). Basically the radial distance is the scalar Euclidean distance between a point and the origin of the system of coordinates.

Distance of two points in polar coordinates

The distance d between two points P₁ and P₂ with polar coordinates (r₁, θ₁) and (r₂, θ₂) is given by the polar distance formula:

$d = \sqrt{r_1^2 + r_2^2 - 2 r_1 r_2 \cos (\theta_1 - \theta_2)}. \,$

This formula is derived from the law of cosines, applied to the triangle P₁OP₂ in which two sides have lengths r₁ and r₂ and the included angle is θ₁ − θ₂.