How to Use the Cartesian ↔ Polar Coordinate Converter
There are two common ways to describe a point on a plane: Cartesian coordinates (x, y), measured as distances along the x and y axes, and polar coordinates (r, theta), measured as a distance from the origin plus an angle. This tool converts between the two instantly in both directions. Enter x and y in the top section to get r and theta, or enter r and theta (in degrees) below to get x and y.
Converting Cartesian to polar uses r = √(x² + y²) and theta = atan2(y, x), with the angle measured from the positive x-axis, increasing counterclockwise, and shown in the 0-360 degree range. Converting polar to Cartesian uses x = r × cos(theta) and y = r × sin(theta). Both coordinate systems show up constantly — in physics vectors, engineering signal analysis, and rotation math in game development.
Note that the origin (0, 0) is a special case: its distance is 0, but it has no defined direction, so it can't be converted to polar form. Negative coordinates are supported too, and the resulting angle is calculated correctly even past 90 or 270 degrees.
Frequently Asked Questions
It follows the standard math convention: 0 degrees points along the positive x-axis, increasing counterclockwise. Results are shown in the 0-360 degree range.
The origin (0,0) has a distance (r) of 0 but no defined direction, so it can't be converted into polar coordinates, which require an angle.