Polar to Cartesian Converter

About this calculator

Polar coordinates locate a point by a radius r (distance from the origin) and an angle θ measured from a reference axis, while Cartesian coordinates locate the same point with horizontal and vertical distances x and y. The conversion follows directly from basic trigonometry: x = r·cos(θ) and y = r·sin(θ).

This conversion is routine in physics and engineering, where forces, velocities and electromagnetic fields are often measured as a magnitude and direction but need to be added or plotted component-wise. Robotics and navigation systems use it to turn a radar or sonar reading (distance and bearing to a target) into x/y coordinates for mapping, and graphics programmers use it to place points on circular or spiral paths.