Enter the coordinate points of each vertex of a triangle into the calculator. The calculator will evaluate and display the centroid of the triangle.

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## Centroid Formula

The following formula is used to calculate the centroid of a triangle.

Z = [(X1+X2+X3)/3,(Y1+Y2+Y3)/3]

- Where Z is the coordinate points of the centroid
- x1,x2, and x3 are the x-coordinates of the vertices
- y1,y2, and y3 are the y-coordinates of the vertices

To calculate the centroid, add together all of the x-coordinate points, then divide by 3 to give you your centroid x-coordinate, then apply the same process to the y-coordinate points.

## Centroid Definition

A centroid is the average coordinate center of any shape.

## Centroid Example

How to calculate a centroid?

**First, gather the coordinate points of the vertices**Gather both the x and y coordinate points of each vertex.

**Next, sum all of the x coodinates**Add together all of the x coordinates and then divide the answer by 3.

**Next, sum all of the y coordinates**Add together all of the y coordinates and then divide the answer by 3.

**Put the answers from steps 2 and 3 together**The centroid will have an x value equal to that calculated in step 2 and the y value equal to that calculated in step 3.

## FAQ

**What is a centroid?**

A centroid is the average center of any shape. In general, this is most associated with a triangle, but it can be calculated on any polygon with vertices.

**How do you calculate the centroid of any shape?**

The centroid is also known as the average of values of a set of points. In other words, it’s the average of a set of points, weighted by their respective values. Therefore, if you have a shape with 50 points, you could technically calculate the centroid of those points using the same formula as the above bad adding in the additional coordinates.