Free · Mathematics models
Circle Coefficients and Equivalent Forms
Complete the square to connect general, center-radius and parametric circle forms.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
For x²+y²−6x+4y−12=0, the center is (3,−2), the radius is 5 and the diameter is 10.
Center=(−d/2,−e/2); squared radius=(d²+e²)/4−f.
Worked example
Enter these known values and leave the other values blank.
- D
- -6
- E
- 4
- F
- -12
- A
- 3
- B
- -2
- C
- 25
- A
- 3
- B
- -2
- r
- 5
- x
- 3
- y
- -2
- Radius
- 5
- Diameter
- 10
- Area
- 78.5
- Circumference
- 31.4
Assumptions and limitations
- The x² and y² coefficients are both one and there is no xy term. A nonnegative squared radius is required; zero is a degenerate point circle.
- All sign-dependent equation notes retain their original branches; changing a center coordinate updates the coefficients.
- General rotated conics and unequal quadratic coefficients are outside this circle model.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
The x² and y² coefficients are both one and there is no xy term. A nonnegative squared radius is required; zero is a degenerate point circle.
What does this model leave out?
General rotated conics and unequal quadratic coefficients are outside this circle model.
References
Model requirements: Squared radius must be nonnegative.