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Polar Coordinates Calculator

Online polar converter: enter rectangular (x,y) to get the radius r and angle θ.

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r=√(x²+y²), θ=atan2(y,x)
Rectangular (x,y)
x
y

📖 Tutorial | Polar

1. Definition
Relations: x=r cosθ, y=r sinθ; r=√(x²+y²), θ=atan2(y,x).
2. Formula & Notation
r,θRadius, angle
3. Properties & Laws
  • r non-negative;
  • atan2 fixes the quadrant;
  • Pole r=0;
  • Inverse x=r cosθ.
4. Steps
  1. Enter x,y;
  2. Click "To Polar";
  3. Or click "Load Example".
5. Worked Examples
Example: (3,4): r=5, θ≈53.13°.
6. Common Pitfalls
Use atan2, not atan(y/x);
Non-negative r;
Pole is special.

❓ FAQ | Polar

r?
√(x²+y²).
θ?
atan2.
Non-negative?
Yes.
Pole?
r=0.
Example?
5, 53.13°.
Inverse?
cos.