Equation of a Circle Calculator

Your details

Choose how you want to define the circle: by its center and radius, by general-form coefficients, or by three points that lie on it.
The x-coordinate of the center of the circle.
The y-coordinate of the center of the circle.
The radius of the circle (must be greater than zero).
Standard form
(x - 3)² + (y + 2)² = 25

(x - h)² + (y - k)² = r²

General formx² + y² - 6 x + 4 y - 12 = 0
Parametric equationsx = 5 cos(θ) + 3, y = 5 sin(θ) + -2
Center (h, k)(3, -2)
Radius5units
Diameter10units
Area78.5398units²
Circumference31.4159units
x-intercepts(-1.5826, 0) and (7.5826, 0)
y-intercepts(0, -6) and (0, 2)
Domain[-2, 8]
Range[-7, 3]

The equation of the circle is (x - 3)² + (y + 2)² = 25.

  • The standard form equation is (x - 3)² + (y + 2)² = 25.
  • The circle has center (3, -2) and radius 5 units.
  • Its area is 78.5398 square units and its circumference is 31.4159 units.
  • x-intercepts: (-1.5826, 0) and (7.5826, 0).

Next stepTo verify the equation, substitute any known point on the circle and confirm both sides are equal.

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