Free · Geometry and function relationships

Convert a Circle Equation to General Form

Expand the squared offsets of a standard circle equation. C represents radius squared, while h and k are the center coordinates.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For h = 2, k = -3, C = 25, D = -4, E_ = 6, F = -12.

D=−2h; E=−2k; F=h²+k²−C

Worked example

Enter these known values and leave the other values blank.

h
2
k
-3
C
25
D
-4
E
6
F
-12

Assumptions and limitations

  • Expand the squared offsets of a standard circle equation. C represents radius squared, while h and k are the center coordinates.
  • Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
  • Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

Expand the squared offsets of a standard circle equation. C represents radius squared, while h and k are the center coordinates.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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