Triangle Centroid Calculator

About this calculator

The centroid of a triangle — the point where its three medians (lines from each vertex to the midpoint of the opposite side) intersect — is calculated simply by averaging the x-coordinates and y-coordinates of the three vertices. This point always lies inside the triangle and divides each median in a 2:1 ratio from vertex to midpoint.

The centroid represents the triangle's geometric center of mass — if the triangle were a flat, uniform-density plate, it would balance perfectly on a pin placed at the centroid — which makes it essential in engineering statics and structural analysis for locating a shape's center of gravity, in computer graphics for mesh and polygon calculations, and in physics problems involving rotational inertia and balance.

This calculator takes the coordinates of a triangle's three vertices and returns the exact coordinates of its centroid.