# Cartesian and polar two-dimensional coordinate systems

This online calculator converts polar coordinates to cartesian coordinates and vice versa.

A cartesian coordinate system on a plane is chosen by choosing the origin (point O) and axis (two ordered lines perpendicular to each other and meeting at the origin point).

Thus, you can specify any point on a plane by specifying its coordinates, which are distances from the origin to the perpendicular projections of this point to the axis.

There are other coordinate systems in the two-dimensional space, which you can use to specify a point location with two numbers. Most commonly used after cartesian is the polar coordinate system.

The polar coordinate system on a plane is chosen by choosing the original point (pole) and the ray from the pole called the polar axis.

The distance r from any point to the pole is called the polar radius of a point, radial coordinate, or simply radius. The angle between the polar axis and radius is called polar angle, angular coordinate, or azimuth. Radius and azimuth are polar coordinates of a point.

Calculators below convert from polar to cartesian coordinates and vice versa. It is assumed that both systems' origin points are the same, and the polar axis is directed along the positive direction of the x-axis.

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