Cartesian to Polar Coordinates

All math tools

Convert between Cartesian (x, y) and Polar (r, θ) coordinate systems.

Conversion Mode

Cartesian Input

X Coordinate

Y Coordinate

Converted Coordinates

Radius (r)5.0000

Angle (θ)53.13°

Angle (rad)0.9273 rad

About this calculator

Cartesian vs Polar

Cartesian coordinates (x, y) describe a point's location using horizontal and vertical distances from an origin. Polar coordinates (r, θ) describe the same point using the straight-line distance from the origin (radius r) and the angle from the positive x-axis (theta θ). Both systems are useful for different types of mathematical problems.

💡

Pro Tips

In Cartesian coordinates, the origin is (0,0). In Polar, it is r=0.
The angle θ is typically measured counter-clockwise from the positive x-axis.
Make sure you know whether your angle is in degrees or radians. This calculator uses degrees for input/output.

Fun Facts

"René Descartes developed the Cartesian system in the 17th century, linking algebra and geometry."
"Polar coordinates are naturally suited for describing circular and spiral phenomena, like planetary orbits or audio pickups."
"Complex numbers can also be expressed in both rectangular (Cartesian) and polar forms."

Formula: x = r·cos(θ), y = r·sin(θ) | r = √(x²+y²), θ = atan2(y, x)