By Zencalcy Editorial TeamLast reviewed About us
Convert (r, θ) ↔ (x, y) in both directions. Polar suits rotations and spirals; Cartesian suits grids and screens. Angles in degrees or radians, normalized to [0°, 360°).
Both directions, degrees or radians, with worked examples.
x = r·cos θ, y = r·sin θ · r = √(x²+y²), θ = atan2(y, x)
| Symbol | Meaning |
|---|---|
| r | Radius (≥ 0) |
| θ | Angle from +x axis |
(5, 53.13°) → (3, 4). Back: (3,4) → r = 5, θ ≈ 53.130102°.
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atan2(y,x) resolves the correct quadrant, unlike plain arctan(y/x) which confuses opposites.
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Content updated: September 2026