Baricentro do Triângulo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)
About this calculator
This calculator determines the centroid (barycenter) of a triangle in the Cartesian plane. The centroid is the intersection point of the three medians, calculated as the arithmetic mean of the vertices' coordinates. Simply enter the (x, y) coordinates of each vertex and the result is displayed instantly.
The formula is straightforward: for vertices A(x1, y1), B(x2, y2) and C(x3, y3), the centroid G has coordinates ((x1+x2+x3)/3, (y1+y2+y3)/3). This point divides each median in a 2:1 ratio and is the triangle's center of mass.
Use this calculator in analytic geometry problems, physics (center of mass of a uniform triangular lamina) or engineering. It is useful for finding the center of triangular shapes in projects or school exercises.
Caution: ensure the points are not collinear, as degenerate triangles have no centroid. Coordinates must be numeric; avoid letters or symbols. The result is exact for integer or decimal coordinates.
Frequently asked questions
What is the centroid of a triangle?
It is the intersection point of the three medians, also called the barycenter. It divides each median in a 2:1 ratio.
How do I calculate the centroid manually?
Add the x-coordinates of the three vertices and divide by 3; do the same for the y-coordinates. The result is the centroid.
Is the centroid always inside the triangle?
Yes, the centroid of any non-degenerate triangle is always located inside the triangle.
Can I use this calculator for triangles in 3D space?
No, this calculator is for 2D coordinates only. For 3D, you would need to include the z-coordinate.
What happens if the points are collinear?
If the vertices are on a straight line, the triangle is degenerate and the centroid is not defined. The calculator may give a result, but it is geometrically meaningless.