Cut a triangle out of stiff cardboard and balance it on a pencil tip — the tip lands under one magic point every time: the centroid. It is a shape's geometric center, the point where it would balance perfectly if cut from uniform material. For a triangle there is a beautifully simple rule: average the x-coordinates of the three corners, then average the y-coordinates, and that ordered pair is the centroid. A triangle with corners at (0, 0), (6, 0), and (3, 6) has its centroid at (3, 2) — one-third of the way up from the base.

Every median of the triangle passes through this point, and the centroid always divides each median in a 2-to-1 ratio. Steel fabricators use it to pick the lift point for a plate so a crane hoists it level; sign makers use it to place the mounting bracket so a hanging sign does not tilt; geometry students meet it as one of the triangle's four classic centers. For uniform-density shapes the centroid and the center of mass coincide — but for anything with uneven weight, the center of mass drifts away from the centroid toward the heavy side.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Centroid 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.