Cartesian to Polar Calculator

Math

Convert Cartesian coordinates (x, y) to polar coordinates (r, θ) and vice versa.

Formula

Cartesian→Polar: r = √(x²+y²), θ = atan2(y,x); Polar→Cartesian: x = r·cos(θ), y = r·sin(θ)
  • atan2(y,x) gives angle in correct quadrant (range: −180° to 180°).
  • θ = 0° points in the positive x direction.
  • Positive θ is counterclockwise from positive x-axis.

Cartesian (3, 4) to Polar

Inputs
  • Convert: cart2polar
  • x (or r): 3
  • y (or θ in degrees): 4

r = √(9+16) = 5. θ = atan2(4,3) ≈ 53.13°.

Frequently asked questions

What is the formula for r?
r = √(x² + y²) — the distance from the origin (Pythagorean theorem).
Why use atan2 instead of arctan?
atan2(y,x) correctly identifies the quadrant, giving angles from -180° to 180°. arctan alone only gives -90° to 90°.
In what quadrant does the angle land?
Quadrant I (x>0,y>0): 0–90°; II (x<0,y>0): 90–180°; III (x<0,y<0): -180 to -90°; IV (x>0,y<0): -90 to 0°.
Can r be negative?
In polar coordinates, r is conventionally non-negative. A negative r points in the opposite direction.