# Centroid Calculator

## What is centroid?

The centroid is the point of intersection of medians of triangle. It is the point on which the whole mass of object is assume to be concentrated. If we want to balance an object on single pin, this is the point on which we can balance the object. The median is the line with joins the mid point of side and the opposite vertex of triangle.

## What is the centroid formula for a triangle?

Let us assume a triangle ∆ABC, which has three vertex A, B and C. The co-ordinates of vertex are A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3},y_{3}). The centroid of tringle is calculated as follow :

**G = [ (x _{1} + x_{2} + x_{3}) / 3 , (y_{1} + y_{2} + y_{3}) / 3]**

## What is the formula for the centroid?

The centroid formula can be generalized for any object. Centroid is the arithmetic mean of all points of a shape.

**G _{x} = (x_{1} + x_{2} + x_{3} +... + x_{k} ) / k **

G_{y} = (y_{1} + y_{2} + y_{3} +... + y_{k} ) / k

## Centroid of a set of points

The Centroid of set point can be calculated as the mean of all points.

**G _{x} = (x_{1} + x_{2} + x_{3} +... + x_{k} ) / k **

G_{y} = (y_{1} + y_{2} + y_{3} +... + y_{k} ) / k

## How to construct the centroid in a triangle?

Follow the steps to construct the centroid of triangle :

- Draw the perpendicular bisectors of any two sides of triangle. Then find the point of intersection of those perpendiculars.
- Draw the median by connecting the midpoint and the opposite vertex.
- The intersection of this medians will give the centroid of triangle.