Center of Mass Calculator
Find the center of mass for your particle system with this center of mass calculator.
Vertices
| # | x | y |
|---|---|---|
| 1 | 0 | 0 |
| 2 | 6 | 0 |
| 3 | 6 | 4 |
| 4 | 0 | 4 |
The formula
centroid = the average of the vertex coordinates
Two different centroids
For a triangle these coincide, which is why the distinction is easy to miss. For anything else they differ: the vertex average treats the corners as equal point masses, while the area centroid is where a cut-out of the shape would balance. A long thin quadrilateral with two corners bunched together shows the gap clearly.
Area scales with the square
Double every length in a flat shape and the area quadruples; triple them and it grows ninefold. Perimeter, being a length, scales in step with the sides. That mismatch is why bigger shapes enclose proportionally more area per unit of edge — and why a circle, having no corners at all, encloses the most area for a given perimeter of any shape.
Units
Whatever unit you enter, the area comes out in that unit squared and the perimeter in the unit itself. The calculator is unit-agnostic — enter centimetres and read cm and cm², or feet and read ft and ft². Just do not mix units between fields.