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General Form Circle Calculator.

Convert x² + y² + Dx + Ey + F = 0 into center, radius, area, and circumference.

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01

Set your values

Results update as you type.

centerX: 3

centerX

0.00000000
centerY: -2

centerY

0.00000000
radius: 4

radius

0.00000000
area: 50.26548246

area

0.00000000
circumference: 25.13274123

circumference

0.00000000

Results update automatically as you type.

Convert x² + y² + Dx + Ey + F = 0 into center, radius, area, and circumference.

Use Cases

Convert general form to standard form

Quickly transform a circle equation from general form to center-radius form for graphing or further analysis.

Example: Given x² + y² - 6x + 4y - 12 = 0, enter D=-6, E=4, F=-12 to get center (3, -2) and radius 5.

Verify circle properties

Check the center and radius of a circle described by a general equation, useful for geometry homework or design.

Example: For x² + y² + 2x - 8y + 8 = 0, enter D=2, E=-8, F=8 to find center (-1, 4) and radius 3.

Frequently Asked Questions

How do I use the General Form Circle Calculator?
Enter the coefficients D, E, and F from your circle equation in general form (x² + y² + Dx + Ey + F = 0). The calculator will compute the center (h, k) and radius r using the formulas h = -D/2, k = -E/2, and r = sqrt((D/2)² + (E/2)² - F).
What if the equation is not in standard general form?
Ensure the equation is written as x² + y² + Dx + Ey + F = 0 with coefficients of x² and y² equal to 1. If they are not 1, divide the entire equation by that coefficient first, then enter the resulting D, E, and F.
Can the calculator handle equations that do not represent a real circle?
The calculator will compute a value for r, but if (D/2)² + (E/2)² - F is negative, the equation does not represent a real circle (no real points). The calculator will indicate this by showing a negative value under the square root.

Tips & Common Mistakes

Tips

  • Make sure the coefficients of x² and y² are both 1 before entering D, E, and F.
  • Double-check the signs of D, E, and F. For example, in x² + y² - 4x + 6y - 3 = 0, D = -4, E = 6, F = -3.
  • The radius is always positive. If the value under the square root is negative, the equation does not represent a real circle.
  • Use the results to quickly sketch the circle by plotting the center and using the radius to draw the circle.

Common Mistakes to Avoid

  • Forgetting to divide the equation by the coefficient of x² or y² if it is not 1, leading to incorrect D, E, and F.
  • Misinterpreting the sign of the center coordinates: the center is (-D/2, -E/2), not (D/2, E/2).
  • Entering the constant term with the wrong sign: F is the constant term in the equation x² + y² + Dx + Ey + F = 0, so if the equation has a negative constant, F is negative.

Last updated: August 13, 2026