Cartesian to Polar Coordinate Converter

Transform Cartesian coordinates (x, y) into Polar coordinates (radius r, angle θ) and visualize the conversion.

Enter Cartesian Coordinates

Input the x and y values to convert them into polar coordinates.

X Coordinate (x)

Y Coordinate (y)

Visualization

Graphical representation of Cartesian to Polar conversion.

Polar Coordinates Results

Radius (r)

Angle (θ) in radians

Angle (θ) in degrees

Understanding Cartesian to Polar Coordinates

In mathematics, the Cartesian coordinate system is used to uniquely determine each point in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular oriented lines, measured in the same unit of length. To represent the same point in polar coordinates, we use a distance from a reference point (origin) and an angle from a reference direction.

The conversion formulas are:

Radius (r): $$\sqrt{x^2 + y^2}$$
Angle (θ): $$atan2(y, x)$$ (in radians)

This tool helps you convert Cartesian coordinates to polar coordinates, providing both numerical results and a visual representation. Polar coordinates are particularly useful in situations where the system exhibits radial symmetry.

Learn more about coordinate systems on Wikipedia and Polar Coordinates.