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Triangle Circumcenter Calculator

Work out triangle circumcenter instantly with clear inputs, formula shown and shareable results.

About Triangle Circumcenter Calculator

The circumcentre is equidistant from all three vertices and is found where the perpendicular bisectors of the sides meet. Solving the two bisector equations gives the closed form used here.

Formula

Circumcentre

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

Worked example

With the default values below, Triangle Circumcenter Calculator returns Circumcentre of (3, 4). Change any input above and every figure here is recalculated in your browser.

Inputs used

Vertex A (x, y)
0, 0
Vertex B (x, y)
6, 0
Vertex C (x, y)
0, 8

Results

Circumcentre
(3, 4)
Circumcentre x
3.0000
Circumcentre y
4.0000
Circumradius R
5.0000

Step by step

  1. 1Values used
  2. 2Circumcentre
  3. 3Circumcentre= (3, 4)
  4. 4Circumcentre x= 3.0000
  5. 5Circumcentre y= 4.0000
  6. 6Circumradius R= 5.0000

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

Can the circumcentre lie outside the triangle?

Yes. For an obtuse triangle it falls outside, and for a right triangle it sits exactly on the midpoint of the hypotenuse.

What does D = 0 mean?

It means the points are collinear, so no unique circle passes through all three.

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