Circle Equation Calculator
Go back and forth between a circle's center, radius and equation. Enter the center and radius to get the standard and general forms - or enter D, E and F to recover the center and radius from any equation.
A. Equation from center and radius
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B. Center / radius from general form: x^2 + y^2 + Dx + Ey + F = 0
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How to use
- In Section A, enter the center (h, k) and radius — both standard and general forms are created.
- In Section B, enter D, E, F of the general form — the center and radius come back out.
- Both sections can also be used to check each other.
Tips
- The standard form (x-h) squared + (y-k) squared = r squared reads the center and radius directly.
- To expand the general form, complete the square on the x and y terms.
- Use Section B to double-check answers you worked out by hand.
- A negative r squared means the equation does not describe a real circle.
Note: Standard form: (x - h)^2 + (y - k)^2 = r^2. Expanding the general form and comparing coefficients gives D = -2h, E = -2k, F = h^2 + k^2 - r^2.