What is standard form?
(x−h)²+(y−k)²=r² with center (h,k) and radius r.
Equation of a Circle Calculator
Write the standard and general forms of a circle from center (h,k) and radius r.
Enter center and radius
Provide h, k, and a positive radius r.
About this calculator
How to use Equation of a Circle Calculator, plus the formulas and logic behind the results.
Tool description
Standard form highlights the center and radius. Expanding yields the general form x² + y² + Dx + Ey + F = 0.
How to use
- Enter the center coordinates.
- Enter a positive radius.
- Select Calculate.
- Copy the standard or expanded equation.
Formulas & reference
(x − h)² + (y − k)² = r²Expanded: x² + y² − 2hx − 2ky + (h² + k² − r²) = 0
Circle equation tips
- Center is (h,k)
- Radius is √(right-hand side) in standard form
- General form has equal x² and y² coeffs
- No xy term for a circle aligned to axes
Calculation logic
Builds standard form as text and expands algebraically into general form coefficients.
Radius must be positive. r = 0 would be a single point, not a circle here.
Equation of a Circle Calculator FAQ
Common questions about this calculator and how to use the results.
What is general form?
x²+y²+Dx+Ey+F=0 after expanding.
How do I read the center?
From standard form, opposite the signs inside the parentheses.
Can the center be at the origin?
Yes—then x² + y² = r².
Must r be positive?
Yes for a proper circle in this tool.
Does this solve for intersections?
No—it writes the circle equation from center and radius.