Circle Equation Calculator
Derive the standard and general equations of a circle from its center and radius.
About Circle Equation Calculator
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
Worked example
With the default values below, Circle Equation Calculator returns Standard Form of (x − 3)² + (y − -2)² = 5². Change any input above and every figure here is recalculated in your browser.
Inputs used
- Center x (h)
- 3
- Center y (k)
- -2
- Radiusminimum 0
- 5
Results
- Standard Form
- (x − 3)² + (y − -2)² = 5²
- General Form
- x² + y² + -6x + 4y + -12 = 0
- r²
- 25.0000
Step by step
- 1Standard form= (x − 3)² + (y − -2)² = 5²
- 2Expand to general form= x² + y² + -6x + 4y + -12 = 0
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.