What Is a Centroid?
The centroid is the geometric center of a shape — the point where it would balance perfectly if made from a uniform material. For a triangle, the centroid is located at the intersection of its three medians (lines from each vertex to the midpoint of the opposite side).
Centroid = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
The centroid divides each median in a 2:1 ratio from the vertex.
Properties of the Centroid
- Always lies inside the triangle
- Divides each median in ratio 2:1
- Is the center of mass for uniform density
- Is equidistant from the three medians
Applications
Centroids are used in engineering (structural balance points), physics (center of mass), computer graphics (mesh calculations), robotics (balance), and architecture (load distribution).
How to Use
Enter the x,y coordinates of your triangle's three vertices. The calculator instantly computes the centroid coordinates.
Beyond Triangles
For polygons with more than 3 vertices, the centroid calculation becomes more complex, involving area-weighted averages. For simple shapes, it is the average of all vertex coordinates.
Centroid vs Other Centers
Don't confuse the centroid with the circumcenter (equidistant from vertices), incenter (equidistant from sides), or orthocenter (intersection of altitudes). Each serves different purposes.