# Barycentre vs. Centroid — What's the Difference?

Edited by Tayyaba Rehman — By Maham Liaqat — Updated on April 14, 2024

**The barycentre is the center of mass of a system, accounting for mass distribution, whereas the centroid is the geometric center of a shape, independent of material properties.**

## Difference Between Barycentre and Centroid

### Table of Contents

ADVERTISEMENT

## Key Differences

The barycentre (or center of mass) of a system depends on the distribution of mass within that system, making it a critical concept in physics, especially in celestial mechanics, while the centroid is purely a geometric concept used in mathematics to find the center of symmetry in shapes.

In practical applications, engineers use the centroid to determine the geometric center for balancing and design purposes, whereas astronomers use the barycentre to analyze the motions of planets and stars as they interact gravitationally.

The calculation of a barycentre takes into account the masses and positions of all objects within a system, which can result in the barycentre being located outside the physical body of any individual component (as seen in the Earth-Moon system), while the centroid is always within the boundary of the shape unless the shape is concave.

For uniform materials, the centroid and barycentre can coincide because the mass is evenly distributed across the shape. However, if the material or shape is non-uniform, these points will diverge.

Understanding the distinction between these concepts is essential for applications in structural engineering, robotics, astronomy, and any field requiring precise knowledge of how forces and weights distribute across objects.

ADVERTISEMENT

## Comparison Chart

### Definition

Center of mass of an object or system of objects

Geometric center of a solid figure

### Dependency

Depends on mass distribution

Independent of mass, depends only on shape

### Applications

Used in physics, celestial mechanics

Used in geometry, engineering

### Location

May be located outside the object(s)

Always within the boundary of the object

### Example Calculation

Weighted average of positions based on mass

Average of all points' coordinates in a shape

## Compare with Definitions

#### Barycentre

Center of mass of two or more bodies.

The barycentre of the Earth-Moon system is located beneath Earth's surface.

#### Centroid

Independent of material properties.

The centroid of a cardboard cutout is the same as that of a steel version.

#### Barycentre

Calculated using mass and distance.

The barycentre calculation helped determine the stability of the satellite's orbit.

#### Centroid

Used in structural engineering.

The centroid helps in designing balanced structures.

#### Barycentre

Influences orbital dynamics.

The barycentre of the Pluto-Charon system is outside Pluto, affecting their orbital motion.

#### Centroid

Calculated geometrically.

Finding the centroid involved averaging the coordinates of the shape's vertices.

#### Barycentre

Essential in astrophysics.

Understanding the barycentre is crucial for predicting planetary motion.

#### Centroid

Applied in robotics for balance.

Robots use centroid calculations to maintain stability.

#### Barycentre

Varies with mass changes.

A spacecraft's barycentre shifts as it burns fuel.

#### Centroid

Geometric center of a plane figure.

The centroid of a triangle is the point where its medians intersect.

#### Barycentre

The point at the centre of a system; an average point, weighted according to mass or other attribute. The term is usually used in astronomy for the centre of mass about which a system rotates, for example, the moon and the earth rotate about a common point within the earth but not near the centre. Jupiter and the Sun rotate about a common point just outside the surface of the Sun.

#### Centroid

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin.The definition extends to any object in n-dimensional space: its centroid is the mean position of all the points in all of the coordinate directions.While in geometry the word barycenter is a synonym for centroid, in astrophysics and astronomy, the barycenter is the center of mass of two or more bodies that orbit each other.

#### Centroid

See center of mass.

#### Centroid

The point in a system of masses whose coordinates on each dimension are a weighted mean of the coordinates of points on that dimension, the weights being determined by the density function of the system.

#### Centroid

The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.

#### Centroid

The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.

#### Centroid

(of a finite set of points) the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.

#### Centroid

An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.

The centroid of an arbitrary function $f$ is given by $\backslash frac\{\backslash int\; xf(x)dx\}\{\backslash int\; f(x)dx\}$, where the integrals are calculated over the domain of $f$.

#### Centroid

The arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.

#### Centroid

Given a tree of n nodes, either (1) a unique node whose removal would split the tree into subtrees of fewer than n/2 nodes, or (2) either of a pair of adjacent nodes such that removal of the edge connecting them would split the tree into two subtrees of exactly n/2 nodes.

#### Centroid

The center of mass, inertia, or gravity of a body or system of bodies.

#### Centroid

The center of mass of an object of uniform density

## Common Curiosities

#### How does the centroid affect the design of structures?

The centroid is critical in structural design, ensuring objects are balanced and stable under loads.

#### Why might the barycentre of a system be located outside the main body?

If one body in a system is significantly less massive than another, the barycentre can be outside the smaller body.

#### What is the significance of knowing the centroid in manufacturing?

Knowing the centroid is important in manufacturing for quality control and ensuring the balance of products.

#### What is the barycentre used for in astronomy?

In astronomy, the barycentre is used to analyze the orbits of planets and stars within a system.

#### Can the barycentre and centroid of an object be the same?

For objects with uniform density, the barycentre and centroid can coincide.

#### Are the barycentre and centroid relevant in daily life?

Yes, they play a role in various applications from vehicle design to the functioning of natural and artificial satellites.

#### Does the centroid always exist within a shape?

The centroid is always within the boundary for convex shapes but can be outside for certain concave configurations.

#### How is the barycentre calculated?

The barycentre is calculated as a weighted average of the positions of all masses in the system.

#### Can the centroid be used to predict motion?

While the centroid can indicate balance, it does not predict motion, which is influenced by the barycentre.

#### Is the concept of the barycentre only applicable in two-body problems?

No, the concept applies to any number of bodies interacting gravitationally.

#### What happens to the barycentre if the mass distribution changes?

Any change in mass distribution within a system will shift its barycentre accordingly.

#### What tools are used to find the centroid of complex shapes?

Computational tools and integration techniques are often used to find the centroid of complex shapes.

#### How does the centroid relate to the center of gravity?

For uniform gravity fields and uniform material density, the centroid and the center of gravity coincide.

#### How do engineers use the centroid in building construction?

Engineers use the centroid to determine how to distribute loads for optimal structural integrity.

#### What practical examples illustrate the use of the barycentre outside of astronomy?

In biomechanics, understanding the barycentre of the human body helps in improving posture and athletic performance.

## Share Your Discovery

Previous Comparison

Safari vs. JungleNext Comparison

Inca vs. Spanish## Author Spotlight

Written by

Maham LiaqatEdited by

Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.