Centroid Calculator
Find the centroid of a triangle by entering the coordinates of its three vertices. The centroid is the point where all three medians intersect, and this calculator also computes the triangle's area.
The centroid of a triangle is its geometric center, the point where the three medians meet. A median is a line segment from a vertex to the midpoint of the opposite side.
The Formula:
Centroid = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)
It is simply the average of the three x-coordinates and the average of the three y-coordinates.
Example:
For a triangle with vertices at A(0, 0), B(6, 0), and C(3, 9):
- Centroid X = (0 + 6 + 3) / 3 = 3
- Centroid Y = (0 + 0 + 9) / 3 = 3
- Centroid = (3, 3)
Properties of the Centroid:
- The centroid always lies inside the triangle, regardless of the triangle's shape.
- It divides each median into a 2:1 ratio. The centroid is two-thirds of the way from each vertex to the opposite midpoint.
- For a triangle made of uniform material, the centroid is the center of mass (the balance point).
- The centroid is one of the four classical triangle centers, alongside the incenter, circumcenter, and orthocenter.
Area Calculation:
This calculator also computes the triangle's area using the shoelace formula:
Area = |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| / 2