center (3, −2), r = 5
(x − 3)² + (y + 2)² = 25
Algebra and graphing in one workspace
Circle Equation Calculator
Create a circle equation from a center and radius, or convert general form to standard form with completing-the-square steps and a live graph.
Free to use. No account required. Your inputs stay in this browser.
The essential relationship
(x − h)² + (y − k)² = r²
A circle is the set of points a fixed distance r from a center (h, k). Its standard equation exposes the center and radius directly. The calculator keeps full precision internally and rounds only the displayed result.
Worked examples
Follow the numbers, one step at a time
center (0, 0), r = 4
x² + y² = 16
x² + y² − 6x + 4y − 12 = 0
(x − 3)² + (y + 2)² = 25
Built for understanding
More than an answer box
Every result includes the rearranged formula, substituted values, and a reasonableness check. Use the visual to connect the symbols to the measurement.
- Instant, private, browser-based calculation
- Decimal-friendly input and validation
- Responsive layout for phones and classrooms
- Copy-ready answer with units
Method and references
Formula basis
The formula follows standard textbook definitions. Unit symbols follow SI guidance; results are educational estimates, not engineering certification.
- OpenStax Algebra and Trigonometry, Conic Sections
- Desmos graphing conventions
Quick answers
Frequently asked questions
What is standard form?
(x − h)² + (y − k)² = r². The center is (h,k).
Why do signs look reversed?
The form uses x − h and y − k, so a positive center coordinate appears after a minus sign.
How do I convert general form?
Group x and y terms, complete the square twice, and move the constant.
What makes an equation a real circle?
After conversion, r² must be positive. A zero gives a point; a negative value gives no real circle.
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