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Polar Equation of Line Calculator

Online polar line: enter the normal angle α and distance p.

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ρcos(θ−α)=p
Normal, not line direction
Non-negative

📖 Tutorial | Polar Line

1. Definition
The polar line is ρcos(θ−α)=p, with normal angle α and distance p; Cartesian: cosα x+sinα y=p.
2. Formula & Notation
α,pNormal, distance
3. Properties & Laws
  • ρcos(θ−α)=p;
  • Through pole: θ=α;
  • Cartesian cosα x+sinα y=p;
  • p≥0.
4. Steps
  1. Enter α, p;
  2. Click "Equation";
  3. Or click "Load Example".
5. Worked Examples
Example: α=30, p=5: 0.866x+0.5y=5.
6. Common Pitfalls
α is the normal;
p non-negative;
Through pole is θ=const.

❓ FAQ | Polar Line

Form?
ρcos(θ−α)=p.
Through pole?
θ=α.
Cartesian?
cosα x+sinα y=p.
p?
Non-negative.
Example?
0.866x+0.5y=5.
α?
Normal.