# Centroid Calculator

Some points in every figure have to be located precisely because of their significant importance. When it comes to **regular shapes** and **figures**, **Centroid** is one of those points that every student needs to know how to find/locate **inside** the **figure**. Doesn’t matter what is your level of education, you should know **how to find a centroid**.

The process isn’t simple as you have to perform **different calculations** as well as draw **various lines** to find this point. So, the best approach to avoid mistakes and find the location of this point is with the help of the **Centroid Calculator**. This calculator has been designed for this purpose only to help all students who feel it hard to solve various figures. But to use this maths calculator, you need to know what is centroid and the related information of this specific point.

**Table of Contents**

## What is Centroid?

It is the **center of mass** of any regular **object**, **figure**, or **shape**. A **centroid** is a point where the **mass** of the **entire object** or **body lies**. **For example**, the **point** where you can **position** a **pen** on its **tip** will be its **Centroid**.

In **Geometry**, every **regular figure** has such a **point** that we can call its **center of mass**, **centroid**, or a **geometric center**. When you have **positioned** an object on this **point**, it will remain **balanced** and don’t fall unless you have **disturbed** the **equilibrium**. In the following sections, we will show you how you can find the centroid of a shape using a calculator as well as manually.

## Centroid Formula

The **formula** to find the **Centroid** varies from **figure to figure**, **object to object**, and body to body. For the sake of understanding, we can say that the **general formula** to find a **centroid** is the **arithmetic mean** of the **x and y coordinates** of the given **points**. Here is the general formula to find the Centroid of any figure:

^{G}x = (^{x}1 +^{x}2 +^{x}3 +.....^{x}n)/n

^{G}y = (^{y}1 +^{y}2 +^{y}3 +.....^{y}n)/n

These formulas will give you the **x and y coordinates** of the required point. The point formed by combining these coordinates will be the centroid of that specific shape.

## How to calculate the centroid?

As the formula to find this point varies with the shape of the figure or object, the process to calculate it also varies. For your understanding, let us show you **how to find the centroid of the triangle** here.

**Example 1:**

Find the centroid of a triangle whose vertices are: (4,3), (2,5), and (6,7).

**Solution:**

To find the centroid, we need to follow the above-written formula for the triangle. Here is the formula to follow,

Centroid =(^{x}1 +^{x}2 +^{x}3/3 ,^{y}1 +^{y}2 +^{y}3/3)

= (4 + 2 + 6/3 , 3 + 5 + 7/3)

= (12/3 , 15/3)

= (4 , 5)

So, the coordinates of the centroid of the given triangle will be 4 and 5. You can find this point for any regular shape (except a circle) including rectangles, squares, and others.

## How to use the centroid calculator?

You can use this calculator by Calculator’s Bag by following these steps.

**Step 1: **Enter the value of each coordinate in the separate input field.

**Step 2: **The calculator will automatically display an answer on the screen.

### FAQ | Centroid Calculator

**What is the centroid formula for a Triangle? **

The formula to find the centroid of a triangle is given by,

Centroid =(^{x}1 +^{x}2 +^{x}3/3 ,^{y}1 +^{y}2 +^{y}3/3)

**How do you find the centroid of a line? **

The centroid of a line is actually the center of the line. We can find it by bisecting the line.

**What are the special properties of a centroid? **

- This is the point where the mass of an object lies.
- It is the central point of a specific figure.

**Is the centroid always in the middle? **

No, it is not compulsory that the centroid is in the middle. But the centroid must be inside the object or figure for which you are finding it.