# Polar vs. Cartesian Coordinates

## Convert between Cartesian and Polar coordinates.

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)