How to Use the Triangle Circumcenter, Incenter & Centroid Calculator
A triangle has several different "center" points, each with its own geometric meaning. Enter the coordinates of the three vertices and this calculator computes the circumcenter, incenter, and centroid using their exact formulas.
The circumcenter is where the perpendicular bisectors of the three sides intersect — it is equidistant from all three vertices and forms the center of the circle that passes through them. The incenter is where the three angle bisectors meet; it is equidistant from all three sides and is the center of the circle inscribed inside the triangle, calculated as a weighted average of the vertices using the opposite side lengths (a, b, c). The centroid is simply the average of the three vertex coordinates — the point where the triangle would balance if you cut it out and balanced it on a finger.
If the three points lie on a straight line, no actual triangle exists, so the calculation is impossible and the calculator displays an error message. This tool is handy for geometry homework, coordinate geometry practice, and graphics programming where you need a triangle's center points quickly.
Frequently Asked Questions
The circumcenter is where the perpendicular bisectors of the three sides meet, equidistant from all vertices. The incenter is where the three angle bisectors meet, equidistant from all sides. The centroid is the average of the three vertex coordinates, the triangle's balance point.
If the three points lie on a straight line, no triangle is formed, so the circumcenter and incenter cannot be calculated. The calculator shows an error message in that case, so double-check your coordinates.