Polar vs. Cartesian Coordinates

Convert between Polar and Cartesian coordinate systems. Transform 2D coordinates using mathematical formulas to switch between perpendicular Cartesian axes and distance/angle-based Polar coordinates.

Polar vs. Cartesian Coordinates

In the Cartesian system the coordinates are perpendicular to one another with the same unit length on both axes.

2D Cartesian coordinates: (x, y)

A Polar coordinate system is determined by a fixed point (origin or pole) and a zero direction (axis). Each point is determined by an angle and a distance relative to the zero axis and the origin.

Polar coordinates: (r, θ)

Conversion Formulas

Cartesian to Polar:

  • r = √(x² + y²)
  • θ = atan(y / x)

Polar to Cartesian:

  • x = r cos(θ)
  • y = r sin(θ)
Calculator

Inputs

Results

Distance (r)-- units
Angle (θ)-- degrees
Calculator

Inputs

Results

X Coordinate-- units
Y Coordinate-- units