Center of mass of a triangle

Center of mass (center of gravity, barycenter) of a triangle for a triangle that has a uniform density (or at the vertices of which there are equal masses) is located in the centroid of the triangle. The centroid of a triangle is the point of intersection of the medians of the triangle. The centroid is one of the so-called remarkable points of a triangle. For example, in addition to the fact that it is the center of gravity, it also divides each median in a 2:1 ratio, counting from the vertex, and three line segments connecting the vertices of the triangle with the centroid divide this triangle into three equal triangles.

To calculate the position of the center of gravity by the coordinates of the vertices of the triangle, you need to calculate the arithmetic mean of the coordinates of the vertices along the x-axis and along the y-axis, which is what the calculator below does.

Centroid of a triangle

First vertex

x₁

y₁

Second vertex

x₂

y₂

Third vertex

x₃

y₃

Calculation precision

Digits after the decimal point: 2

Calculate

Center of mass

 

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