Polar Coordinate System

The polar coordinate system describes points in space relative to the origin using a combination of radius and angle.
Figure 1: Polar Coordinate System

The Polar Coordinate System describes points in space using a radius and angle relative to the origin. Angles are measured using radians, where a full rotation around the circle is equal to the circle constant τ (tau) or approximately 6.283 radians. By convention angles are measured from what is considered the positive direction in the cartesian-coordinate-system with the positive angle direction as counter-clockwise.

A point is denoted with two variables: which represents the radius corresponding to the point and which represents the angle corresponding to the point.


The point as shown in figure 2 is an example of how a point is defined in the polar coordinate system. The radius defines the distance form the origin and the angle represents the measured angle. In this case the angle is of a full rotation around the circle.

This figure illustrates the polar coordinates point (3, 0.2 τ)
Figure 2: Polar Coordinates Point

Note In math there are two systems for measuring angles: degrees and radians.


Convert Polar to Cartesian Coordinates
Convert Polar to Cartesian Coordinates | Example

To convert a point from the Polar Coordinate System to the Cartesian Coordinate System the functions sine and cosine are used to calculate the x and y component of the corresponding point.

Polar to Cartesian Coordinates
Polar to Cartesian Coordinates | Formula

To convert a point from polar coordinates to cartesian coordinates, the trigonometric functions cosine and sine can be used.