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Parametric Equation of Circle Calculator

Online parametric circle: enter center, radius and the parameter angle θ for a point on the circle.

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x=a+r cosθ, y=b+r sinθ
Center
x
y
r>0
CCW

📖 Tutorial | Parametric Circle

1. Definition
A circle with center (a,b), radius r has x=a+r cosθ, y=b+r sinθ.
2. Formula & Notation
Center, rθ
3. Properties & Laws
  • Parametric form;
  • θ=0 gives (a+r,b);
  • Eliminate for the standard equation;
  • CCW positive.
4. Steps
  1. Enter center, r, θ;
  2. Click "Point";
  3. Or click "Load Example".
5. Worked Examples
Example: r=5, θ=60: (2.5,4.33).
6. Common Pitfalls
Degrees (auto convert);
r>0;
Include center.

❓ FAQ | Parametric Circle

Parameter?
Central angle.
θ=0?
(a+r,b).
Eliminate?
Standard equation.
Direction?
CCW.
Example?
(2.5,4.33).
Full?
0-360.