Free · Circle calculators ⭕

Circle Center from Standard, General or Parametric Form

Find a circle’s center from one of three equation forms, with explicit coefficient meanings.

  • Formula & worked example
  • Private in your browser
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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.

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 (x − 2)² + (y + 3)² = 25, the center is (2, −3). The positive radius is 5.

Standard: (x − A)² + (y − B)² = C; general: x² + y² + Dx + Ey + F = 0; parametric: x = A + r cos t, y = B + r sin t

Worked example

Enter these known values and leave the other values blank.

Standard A: center x
2
Standard B: center y
-3
Standard C: radius squared
25
Circle center x
2
Circle center y
-3

Assumptions and limitations

  • The standard equation is (x − A)² + (y − B)² = C, where C is radius squared. The center is (A, B); C is not the radius.
  • The normalized general equation is x² + y² + Dx + Ey + F = 0. Both squared terms must have coefficient 1 and there must be no xy term. Divide a common nonzero squared-term coefficient out first when applicable.
  • A real nondegenerate circle requires C = (D² + E²)/4 − F > 0. Zero would be a single point, and a negative value gives no real circle; both are excluded.
  • Coordinates use one consistent length scale. Squared radius and area use the square of that scale. A change of coordinate units must be applied consistently to every coefficient.
  • The parametric form uses x = A + r cos t and y = B + r sin t for a full turn. The offsets are the center; the radius is positive.

Common questions

Why is C different from the radius?

The equation equates a sum of squared distances to C. Therefore C = r² and the positive radius is √C; entering r where r² belongs describes a different circle.

Does changing the form change the circle?

Equivalent standard, general and parametric coefficients describe the same circle. The selector chooses the fields for the equation form you know.

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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