General Form of the Equation of a Circle Calculator
The general form of the equation of a circle calculator will convert your circle in general equation form to the standard and parametric equivalents, and determine the circle's center and its properties.
Standard form(x − 2)² + (y + 3)² = 25
General formx² + y² − 4x + 6y − 12 = 0
Centre(2, -3)
Radius5
Circumference31.415927
Area78.539816
Extremes of the circle
| Leftmost point | (-3, -3) |
| Rightmost point | (7, -3) |
| Lowest point | (2, -8) |
| Highest point | (2, 2) |
The formulas
(x − h)² + (y − k)² = r²
Everything follows from the radius
A circle has one degree of freedom, so any single measurement fixes all the others:
d = 2rC = 2πr = πdA = πr² = πd²/4 = C²/4π
Going backwards, r = C/2π and r = √(A/π). The calculator above accepts whichever you happen to have.
Area grows with the square
Double the radius and the circumference doubles, but the area quadruples. That is why a 16-inch pizza is more than twice the food of a an 11-inch one, and why pipe capacity rises so sharply with bore.