Equation of a Circle Calculator
Find standard and expanded circle coefficients from a center and radius or diameter endpoints.
Formula
(x−h)²+(y−k)²=r²; x²+y²+Dx+Ey+F=0; D=−2h; E=−2k; F=h²+k²−r².
Center h ≈ (1) · Center k ≈ (2) · r² ≈ (3)^2 · D ≈ -2×(1) · E ≈ -2×(2) · F ≈ (1)^2+(2)^2-(9)
How to use
- Choose the input mode.
- Enter a center and r, or two diameter endpoints.
- Use h,k,r² or D,E,F in the displayed equation.
Examples
- Diameter (0,0) to (6,8) gives (x−3)²+(y−4)²=25.
Frequently asked questions
What are x₁,y₁?
The center in center mode; the first endpoint in diameter mode.
What about unused fields?
Keep their defaults. Endpoints must differ; r must be positive.
Which units are used?
Use one common coordinate unit. The r² result uses its square.
Sources
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