Polar ↔ Cartesian Coordinate Converter
Convert (x, y) ↔ (r, θ). Polar: r = √(x²+y²), θ = atan2(y, x). Cartesian: x = r·cos θ, y = r·sin θ.
Result
General calculation reads
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How to use this calculator
- Pick direction. Cartesian-to-polar takes (x, y) and returns (r, θ).
- Polar-to-Cartesian takes (r, θ in degrees) and returns (x, y).
- The angle-unit selector switches the displayed θ between degrees and radians.
About this calculator
Two coordinate systems for the same plane. Cartesian (x, y) — perpendicular axes, intuitive for rectangular shapes. Polar (r, θ) — radius from origin + angle from positive x-axis, intuitive for circular shapes and rotation. Conversions: r = √(x²+y²); θ = atan2(y, x) — uses the TWO-argument arctangent so the quadrant is preserved (regular atan(y/x) loses the sign distinction between quadrants II/IV and I/III). x = r·cos θ; y = r·sin θ. Polar is the natural form for orbits, spirals, antenna patterns, and complex-number magnitude/phase representation; Cartesian is the natural form for translation, regular grids, and most CAD work.
Frequently asked
Why atan2 instead of atan(y/x)?+
Is r ever negative?+
What's the angle convention?+
Source?+
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