General Form of the Equation of a Circle Calculator

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Choose which direction to convert. General form is x² + y² + Dx + Ey + F = 0. Standard form is (x - h)² + (y - k)² = r².
The coefficient of x in x² + y² + Dx + Ey + F = 0.
The coefficient of y in x² + y² + Dx + Ey + F = 0.
The constant term in x² + y² + Dx + Ey + F = 0.
Radius
2units

Distance from center to the edge of the circle

Center x (h)2
Center y (k)3
Diameter4units
Area12.5664sq units
Circumference12.5664units
D coefficient-4
E coefficient-6
F constant9
Parametric formx = 2 + 2.0000 cos(α), y = 3 + 2.0000 sin(α)
Standard form(x - 2)^2 + (y - 3)^2 = 4.0000
General formx² + y² - 4x - 6y + 9 = 0

Center (2, 3), radius 2.0000 - circle properties computed from general form.

  • The circle has center (2, 3) and radius 2.0000 units.
  • Its diameter is 4.0000 units, area is 12.5664 square units, and circumference is 12.5664 units.
  • The parametric form is: x = 2 + 2.0000 cos(α), y = 3 + 2.0000 sin(α)

Next stepTo verify, substitute any point on the circle (e.g., (h + r, k)) into both forms and confirm both equations equal zero/r².

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