Polar Cartesian converter

Convert two-dimensional polar and Cartesian coordinates with explicit angle units and correct quadrants.

Your input

Outputs are cleared when the input changes.

Result

Enter your data or use the example, then run the tool.

Worked example

Cartesian (−1,1) gives r=√2 and angle 135°.

r=2, θ=π radians gives (−2,0) within floating-point tolerance; at (0,0), the angle is undefined.

Method

Polar conversion uses x=r cosθ and y=r sinθ. Cartesian conversion uses hypot and atan2 to retain the quadrant.

Angles normalize to [0,360°) or [0,2π). The origin has no polar direction.

Limits

Radius must be non-negative and polar angle magnitude at most 10⁹ in the selected unit. Finite, consistently scaled coordinates only.

Two-dimensional mathematical coordinates; no geographic bearing, map projection or 3D transform. Trigonometric results are approximate.

Sources

OpenStax: polar coordinate conversions

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