Maths & numbers
Circle through three points
Find the circumcentre, radius and equation of the circle through three plane points.
A clear answer. Here’s how.
Translates coordinates relative to A, solves the two perpendicular-bisector equations and returns the centre and radius. Repeated, collinear or numerically near-collinear points do not define a reliable finite circle here. Rejects when the cross-product magnitude is at most 10⁻¹² times the two displacement lengths’ product. Uses one consistent Cartesian length unit.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Point A · x
- 0
- Point A · y
- 0
- Point B · x
- 4
- Point B · y
- 0
- Point C · x
- 0
- Point C · y
- 3
Example result
- Centre x
- 2
- Centre y
- 1.5
- Radius
- 2.5
- Circle equation
- (x − 2)² + (y − 1.5)² = 6.25
- Circumference
- 15.7079632679
- Area (square units)
- 19.6349540849