Circle Equation Calculator
Centre, radius, standard and general form of any circle.
Enter your values
ⓘ Live results
Results
- Standard form
- (x − 3)² + (y + 2)² = 25
- General form
- x² + y² − 6x + 4y − 12 = 0
- Circumference
- 31.4159
- Area
- 78.5398
- Diameter
- 10
- Bounding box
- x from -2 to 8, y from -7 to 3
Quick answer
A circle with centre (h, k) and radius r has the equation (x − h)² + (y − k)² = r², which expands to the general form x² + y² + Dx + Ey + F = 0.
(x − h)² + (y − k)² = r²
How to use the Circle Equation Calculator
- 1Enter the centre coordinates.
- 2Enter the radius.
- 3Copy the standard or general form, whichever your class or CAD tool expects.
Worked example
Using the values the calculator loads with:
Inputs
- Centre x (h)3
- Centre y (k)-2
- Radius r5
Results
- Standard form(x − 3)² + (y + 2)² = 25
- General formx² + y² − 6x + 4y − 12 = 0
- Circumference31.4159
- Area78.5398
- Diameter10
- Bounding boxx from -2 to 8, y from -7 to 3
Frequently asked questions
How do I go from general form back to standard?
Complete the square on the x and y terms; the centre is (−D/2, −E/2) and r² = h² + k² − F.
What if the radius comes out imaginary?
Then the general-form equation has no real circle — it describes an empty set or a single point.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.