How does the Circle Equation Calculator work?

Standard form: (x-h)² + (y-k)² = r² where (h,k) = center, r = radius Then: General form: x² + y² + Dx + Ey + F = 0; convert by completing square Then: From three points: set up three equations, solve system Then: Center = (-D/2, -E/2); radius = √(D²/4 + E²/4 - F).

Can you give an example of how to use the Circle Equation Calculator?

Example: Input center (2,3), r=5 gives a result of (x-2)^2+(y-3)^2=25.

Is the Circle Equation Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Circle Equation Calculator?

Our Circle Equation Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Matematik

Circle Equation Calculator

Circle Equation

Center h

Center k

Radius (r)

Finds circle equation from center and radius or from three points.

Symbol	Name	Unit	Description
D	√(D²/4 + E²/4 - F)	—	√(D²/4 + E²/4 - F)
E	√(D²/4 + E²/4 - F)	—	√(D²/4 + E²/4 - F)
F	0; convert by completing square	—	0; convert by completing square

Difficulty:intermediate

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Did You Know?

Circle is special case of ellipse where both semi-axes equal.

References

›Circle Equation Calculator

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