Every triangle has a secret companion circle passing exactly through all three corners — and the circumcenter is the pinpoint middle of that circle. It is the center of the circumscribed circle, the unique circle threading through a triangle's three vertices. You find it where the perpendicular bisectors of the sides meet — or with coordinates, by solving for the point equidistant from all three corners.

For an acute triangle it sits inside; for a right triangle it lands exactly on the midpoint of the hypotenuse (which is why the hypotenuse of a right triangle is always a diameter of its circumcircle); for an obtuse triangle it falls outside. Surveyors and construction layout crews care because three known points define a circle's center — the same geometry behind trilateration in GPS. Students usually meet the circumcenter alongside the centroid, incenter, and orthocenter as the triangle's four classic centers. This calculator walks through the coordinate computation: enter the vertex values and combine them to locate the center and its radius.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Circumcenter Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.