Circle Equation Calculator
Derive the standard and general equations of a circle from its center and radius.
Inputs
Standard Form
(x − 3)² + (y − -2)² = 5²
General Form
x² + y² + -6x + 4y + -12 = 0
r²
25.0000
Step by step
Standard form
= (x − 3)² + (y − -2)² = 5²
Expand to general form
= x² + y² + -6x + 4y + -12 = 0
How it works
The standard form of a circle with center (h,k) and radius r is (x−h)²+(y−k)²=r². Expanding gives the general form x²+y²+Dx+Ey+F=0.
Formula
Standard Form
(x − h)² + (y − k)² = r²
- h
- Center x-coordinate
- k
- Center y-coordinate
- r
- Radius
Frequently Asked Questions
How do I find center and radius from general form?
Complete the square: h = −D/2, k = −E/2, r = √(h²+k²−F).
What if the radius is zero?
A circle with radius zero is a degenerate case — just a single point at the center.