Circle Equation Calculator
Centre, radius, standard and general form of any circle.
Enter your values
Enter the centre x (h) you are working with.
Enter the centre y (k) you are working with.
Enter the radius r you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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
At a glance
| What it does | Centre, radius, standard and general form of any circle. |
|---|---|
| Category | Math |
| Inputs needed | Centre x (h), Centre y (k), Radius r |
| Main output | Standard form |
| Formula | (x − h)² + (y − k)² = r² |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Centre x (h)
- Enter the centre x (h) you are working with.
- Centre y (k)
- Enter the centre y (k) you are working with.
- Radius r
- Enter the radius r you are working with.
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.
What do I need to enter into the Circle Equation Calculator?
Just 3 values: centre x (h), centre y (k), radius r. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Circle Equation Calculator work out the 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. It applies the formula (x − h)² + (y − k)² = r² and shows the working so you can check each step by hand.
Is the Circle Equation Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.