Circle Through Three Points Calculator

Work out circle through three points instantly with clear inputs, formula shown and shareable results.

About Circle Through Three Points Calculator

Three non-collinear points determine exactly one circle. Its centre is the common intersection of the perpendicular bisectors, obtained in closed form from the determinant of the squared coordinates.

Formula

Circumcentre

D = 2[xA(yB−yC) + xB(yC−yA) + xC(yA−yB)], then Ux and Uy from the squared-length sums

Worked example

With the default values below, Circle Through Three Points Calculator returns Equation of the circle of (x - 3)^2 + (y - 4)^2 = 25. Change any input above and every figure here is recalculated in your browser.

Inputs used

Point A (x, y): 0, 0
Point B (x, y): 6, 0
Point C (x, y): 0, 8

Results

Equation of the circle: (x - 3)^2 + (y - 4)^2 = 25
Centre: (3, 4)
Radius: 5.0000
Enclosed area: 78.5398

Step by step

1Values used
2Circumcentre
3Equation of the circle= (x - 3)^2 + (y - 4)^2 = 25
4Centre= (3, 4)
5Radius= 5.0000
6Enclosed area= 78.5398

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For (0,0), (6,0), (0,8)?

This is a right triangle, so the centre is the hypotenuse midpoint (3, 4) and the radius is 5.

What if the points are collinear?

The determinant D is zero and no finite circle exists; the 'circle' degenerates to a straight line.