Maths Help UK

Polar coordinates

(r, θ) instead of (x, y). r = √(x²+y²); tanθ = y/x.

Enter values above to calculate.

Polar uses distance from origin and angle from positive x-axis. Curves like circles, cardioids and roses are simpler in polar form.

Worked examples
(2, π/3): x = 2 cos π/3 = 1; y = 2 sin π/3 = √3.
r = 2 cosθ is a circle of radius 1 centred at (1, 0).
r = 1 + cosθ is a cardioid.

Frequently asked questions

Negative r?
Convention: (−r, θ) = (r, θ + π).
Multiple representations?
Yes — (r, θ + 2π) is the same point. Choose 0 ≤ θ < 2π for uniqueness.