Circle Equation Calculator
Enter center (h,k) and radius r — or the general form coefficients D, E, F — to get both standard and general equations of the circle.
Enter the center coordinates and radius to find both equation forms.
Enter coefficients for x²+y²+Dx+Ey+F=0.
Leave a field blank to treat it as 0.
Standard Form
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(x − h)² + (y − k)² = r²
General Form
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x² + y² + Dx + Ey + F = 0
Derived Values
Center
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Radius
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Diameter
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Area
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Circumference
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Summary
Enter center (h,k) and radius r — or the general form coefficients D, E, F — to get both standard and general equations of the circle.
How it works
- Choose a direction: "Center & Radius → Equation" or "General Form → Standard Form".
- For center/radius mode, enter the x and y coordinates of the center plus the radius.
- The standard form (x−h)²+(y−k)²=r² is assembled directly from your inputs.
- The general form x²+y²+Dx+Ey+F=0 is derived by expanding the standard form.
- For general form mode, enter D, E, and F; the calculator completes the square to recover h, k, and r.
- Results update instantly as you type.
Use cases
- Verify homework answers for conic-section problems.
- Convert a circle equation between standard and general form for exam prep.
- Find the center and radius of a circle given its general equation.
- Check the equation of a circle drawn on a coordinate plane.
- Quickly derive the general form coefficients for graphing software input.
Frequently Asked Questions
Last updated: 2026-06-13 ·
Reviewed by Nham Vu