# Convert between Polar and Cartesian Coordinates

## Cartesian and Polar coordinate converting

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes.

Cartesian coordinates in the figure below: (2,3)

A Polar coordinate system is determined by a fixed point, a origin or pole, and a zero direction or axis. Each point is determined by an angle and a distance relative to the zero axis and the origin.

Polar coordinates in the figure above: (3.6, 56.31)

Polar coordinates can be calculated from Cartesian coordinates like

r = (x^{2}+ y^{2})^{1/2}(1)

where

r = distance from origin to the point

x = Cartesian x-coordinate

y = Cartesian y-coordinate

θ = atan(y / x)

= tan^{-1}(y / x) (2)

where

θ = angle relative to the zero axis (degrees)

Cartesian coordinates can be calculated from Polar coordinates like

x = r cos(θ) (3)

y = r sin(θ) (4)