Calculators
Triangle Circumcenter Calculator
Find a triangle’s circumcenter and circumcircle radius from three Cartesian vertices, privately in your browser.
Find the circle passing through three triangle vertices.
The circumcenter is the intersection of the perpendicular bisectors and is equidistant from all three vertices. Translate A to the origin, with u = B − A and v = C − A. Let D = 2(uₓvᵧ − uᵧvₓ). The offset from A is ((|u|²vᵧ − |v|²uᵧ)/D, (uₓ|v|² − vₓ|u|²)/D). Add A to obtain the center; the offset length is the circumradius. For A = (0, 0), B = (6, 0), C = (0, 9), the center is (3, 4.5) and radius is approximately 5.4083269132 units. The center lies inside an acute triangle, at the hypotenuse midpoint for a right triangle, and outside an obtuse triangle. Use consistent units on a flat Cartesian plane, not latitude and longitude. Signed decimals and scientific notation are accepted; coordinate magnitudes must be zero or 1e-100 to 1e100. Repeated vertices and triangles whose doubled area is at most 1e-12 times the longest side squared are rejected. Normalized arithmetic limits overflow, but small differences between large coordinates can be lost. Results display up to 12 significant digits. Inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is the circumcenter calculated?
Solve for the point equally distant from all three vertices by intersecting their perpendicular bisectors. The page explains the translated coordinate formula.
Can the circumcenter lie outside the triangle?
Yes. It lies outside an obtuse triangle, inside an acute triangle, and at the hypotenuse midpoint of a right triangle.
Is the circumcenter the same as the incenter?
The circumcenter is equidistant from vertices; the incenter is equidistant from sides. They generally differ, but coincide in an equilateral triangle.
Why are some vertices rejected?
Repeated or collinear vertices do not determine a unique circumcircle. Nearly collinear triangles are rejected because their centers cannot be resolved reliably.
Are coordinates uploaded?
No. The calculator runs locally in your browser.