Centroid of a Triangle Calculator

Centroid Calculator

This online calculator finds the centroid of a triangle in 2 dimensions. It means you can compute the center point of the triangle known as a centroid.

What is a Centroid?

A centroid is a point where the three medians of a triangle intersect each other. If a polygon is fixed at its centroid, the figure becomes geometrically balanced. 

A very common mistake people make is that they think the centroid divides medians in half. Actually, the centroid is the point that divides medians in the ratio of 2:1.

Centroid of a Triangle Formula

The formulas of the centroid are different for polygons. The formula used to compute the centroid of a triangle is:

Centroid = X₁ + X₂ + X₃ / 3 , Y₁ + Y₂ + Y₃ / 3

It is very similar to the formula of the midpoint. It is important to note that the answer is in the form of a point.

How to calculate the Centroid of a Triangle?

Example:

The points A, B, and C of a triangle are (1,2), (2,3), and (3,1) respectively. Find the centroid of this triangle.

Solution: 

Step 1: Write all the vertices. 

X₁ = 1 , Y₁ = 2 

X₂ = 2 , Y₂ = 3

X₃ = 3 , Y₃ = 1

Step 2: Add all the X vertices and Y vertices.

= X₁ + X₂ + X₃ , Y₁ + Y₂ + Y₃ 

= 1 + 2 + 3 , 3 + 2 + 1

= 6, 6

Step 3: Divide both sums by 3.

= 6/3 , 6/3

= 2, 2 

Hence, the centroid of this triangle exists on point (2,2) on the cartesian plane.