Circumcenter Calculator
Find a triangle’s circumcenter and circumradius from three Cartesian vertices.
Formula
With u=B−A, v=C−A, d=2(uₓvᵧ−uᵧvₓ): O=A+((vᵧ|u|²−uᵧ|v|²)/d, (uₓ|v|²−vₓ|u|²)/d); R=|O−A|.
Center x ≈ (0)+(2) · Center y ≈ (0)+(1.5) · Circumradius ≈ sqrt((2)^2+(1.5)^2)
How to use
- Enter the three vertices.
- Use one common coordinate scale.
- Read center coordinates and radius.
Examples
- (0,0), (4,0), (0,3) give center (2,1.5) and radius 2.5.
Frequently asked questions
Can points lie on one line?
No. Collinear or repeated points do not define a unique circle.
Is the center always inside?
No. It lies outside an obtuse triangle.
What about nearly collinear points?
The circle can be enormous and sensitive to rounding; use better precision for such data.
Sources
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