# Centroid Calculator

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Lets first understand, what is a centroid of a triangle and how we can find the centroid of any triangle?

Centroid

The centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure.

In Astrophysics, we use barycenter for centroid. The barycenter is the center of mass of two or more bodies that orbit each other. In physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, its center of mass is the same as the centroid of its shape.

Properties of centroid

1. The geometric centroid of a convex object always lies in the object.

2. A non-convex object might have a centroid that is outside the figure itself.

3. The geometric centroid of an object lies in the intersection of all its hyperplanes of symmetry.

4. The centroid of a parallelogram is the meeting point of its two diagonals.

Centroid of a triangle

The centroid of a triangle is the intersection of the three medians of the triangle.

Let the coordinates of the three vertices of the triangle be \(A(X_1,Y_1)\), \(B(X_2,Y_2)\) and \(C(X_3,Y_3)\).

Then, the coordinates of the centroid is given by

$$G\left(\dfrac{X_1+X_2+X_3}{3},\dfrac{Y_1+Y_2+Y_3}{3}\right).$$For calculating the centroid of any triangle using above centroid calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.