Centroid vs. Center — What's the Difference?
By Tayyaba Rehman — Updated on November 2, 2023
The centroid is the geometric center of a plane figure or solid, while the center is a general term for the middle point of a shape or object.
Difference Between Centroid and Center
Table of Contents
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Key Differences
The centroid refers specifically to the point where the geometric object's mass would balance perfectly if it were made of a uniform material. It's a term that is often used in the fields of geometry, physics, and engineering. In a two-dimensional shape, the centroid is the intersection of all straight lines that divide the shape into two parts of equal moment about the line.
The center, however, can have various meanings depending on the context. In geometry, it can refer to the middle of a circle or sphere, known as the center of rotation or the point equidistant from all edges. In a broader sense, it's simply the middle point or main area of an object, group, or activity.
The centroid is always located within the boundaries of a simple, closed figure and can be calculated using mathematical methods involving integrals or summations of coordinates. The position of the centroid depends on the shape's geometry and is not necessarily the same as the center of mass unless the material is uniform.
The center is a term that is more accessible and commonly understood, while the centroid requires a technical understanding to identify accurately. In practice, the center of an object might be found by sight or estimation, but finding the centroid would typically involve calculations.
Both the centroid and the center have significance in their respective fields. For instance, in construction and structural engineering, knowing the location of the centroid helps in determining how forces like gravity will interact with a body. Meanwhile, knowing the center of an object might be important for balance, aesthetics, or function.
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Comparison Chart
Definition
Point where uniform mass would balance
Middle point of a shape or object
Calculation
Through geometric or integral methods
Often estimated or found by symmetry
Discipline
Geometry, physics, and engineering
General usage in various fields
Location
Always within the shape
Can be inside or outside (e.g., circles)
Usage
Used in precise calculations and technical fields
Used broadly, often non-technically
Compare with Definitions
Centroid
A centroid is the center of mass of a geometric object.
The centroid of a triangle is found by intersecting its medians.
Center
The center is the middle point of a shape.
The wheel rotates around its center.
Centroid
In physics, the centroid represents the point of an object’s uniform weight distribution.
Engineers calculated the centroid to ensure proper balance.
Center
In mathematics, the center is the equidistant point from all points on a circumference.
The center of the circle is marked by a small dot.
Centroid
The centroid of a uniform-density object aligns with its center of gravity.
For this flat plate, the centroid corresponds with its gravitational center.
Center
The center can refer to a hub or a place of importance.
Downtown is the center of our city's cultural events.
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.
Center
A point or place that is equally distant from the sides or outer boundaries of something; the middle
The center of a stage.
Centroid
Centroid calculation is essential in static equilibrium problems.
Identifying the centroid helps in analyzing the object's stability.
Center
A point equidistant from the vertices of a regular polygon.
Centroid
The centroid of a complex shape can be found using calculus.
He used integral calculus to determine the shape’s centroid.
Center
A point equidistant from all points on the circumference of a circle or on the surface of a sphere.
Centroid
See center of mass.
Center
A point around which something rotates or revolves
The sun is the center of our solar system.
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.
Center
A part of an object that is surrounded by the rest; a core
Chocolates with soft centers.
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.
Center
A place where a particular activity or service is concentrated
A medical center.
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.
Center
A point of origin, as of influence, ideas, or actions
A center of power.
A center of unrest.
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.
Center
An area of dense population
A metropolitan center.
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 is given by , where the integrals are calculated over the domain of .
Center
A person or thing that is the chief object of attention, interest, activity, or emotion.
Centroid
The arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.
Center
A person, object, or group occupying a middle position.
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.
Center
Often Center A political group or a set of policies representing a moderate view between those of the right and the left.
Centroid
The center of mass, inertia, or gravity of a body or system of bodies.
Center
(Physiology) A group of neurons in the central nervous system that control a particular function
The vasomotor center.
Centroid
The center of mass of an object of uniform density
Center
(Sports) A player who holds a middle position on the field, court, or forward line in some team sports, such as hockey and basketball.
Center
(Football) An offensive lineman who snaps the ball to begin a play, usually positioned in the middle of the line.
Center
(Baseball) Center field.
Center
A small conical hole made in a piece of work with a center punch so that a drill can be accurately positioned within it.
Center
A bar with a conical point used to support work, as during turning on a lathe.
Center
A centering.
Center
A point in space equidistant from all the points on an arch or on a portion of an arch.
Center
To place in or at the center
Centered the vase on the table.
Center
To direct toward a center or central point; concentrate or focus
Tried to center the discussion on the main issues.
Center
To pass (a ball or puck) toward the center of a playing area.
Center
To play as a center on (a line), as in ice hockey.
Center
(Football) To hike (the ball) to begin a down.
Center
To be concentrated; cluster
The epidemic centered in the urban areas.
Center
To have a central theme or concern; be focused
Her novels center on the problems of adolescence.
Center
(Sports) To play as a center.
Center
The point in the interior of a circle that is equidistant from all points on the circumference.
Center
The point in the interior of a sphere that is equidistant from all points on the circumference.
Center
The middle portion of something; the part well away from the edges.
Center
(obsolete) The innermost point of the Earth, or the Earth itself, as the center or foundation of the Universe; the center or foundation of the Universe abstractly.
Center
(geometry) The point on a line that is midway between the ends.
Center
(geometry) The point in the interior of any figure of any number of dimensions that has as its coordinates the arithmetic mean of the coordinates of all points on the perimeter of the figure (or of all points in the interior for a center of volume).
Center
The subgroup (respectively, subring), denoted Z(G), of those elements of a given group (respectively, ring) G that commute with every element of G.
Center
A place, especially a building or complex, set aside for some specified function or activity.
Shopping center, convention center, civic center, garment center, Lincoln Center for the Performing Arts, Rockefeller Center
Center
(politics) The ensemble of moderate or centrist political parties.
Center
The venue in which the head of government in a centralized state is situated.
Center
A topic that is particularly important in a given context, the element in a subject of cognition, volition or discussion that is perceived as decisive.
The center of the controversy
The center of attention
Center
(sports) A player in the middle of a playing area.
Center
(basketball) The player, generally the tallest, who plays closest to the basket.
Center
(ice hockey) The forward that generally plays between the left wing and right wing and usually takes the faceoffs.
Center
The person who holds the ball at the beginning of each play.
Center
(netball) A player who can go all over the court, except the shooting circles.
Center
(soccer) A pass played into the centre of the pitch.
Center
(rugby) One of the backs operating in a central area of the pitch, either the inside centre or outside centre.
Center
A certain mechanical implement functioning in the middle of a whole apparatus
Center
(architecture) A temporary structure upon which the materials of a vault or arch are supported in position until the work becomes self-supporting.
Center
(engineering) One of the two conical steel pins in a lathe, etc., upon which the work is held, and about which it revolves.
Center
(engineering) A conical recess or indentation in the end of a shaft or other work, to receive the point of a center, on which the work can turn, as in a lathe.
Center
The ring in the gambling game two-up in which the spinner operates.
Center
Of, at, or related to a center.
Center
(transitive) To cause (an object) to occupy the center of an area.
He centered the heading of the document.
Center
(transitive) To cause (some attribute, such as a mood or voltage) to be adjusted to a value which is midway between the extremes.
Center
(transitive) To give (something) a central basis.
Center
(intransitive) To concentrate on (something), to pay close attention to (something).
The plot centers on the life of a working-class family.
The discussion centered around the recent issues.
Center
(engineering) To form a recess or indentation for the reception of a center.
Center
A point equally distant from the extremities of a line, figure, or body, or from all parts of the circumference of a circle; the middle point or place.
Center
The middle or central portion of anything.
Center
A principal or important point of concentration; the nucleus around which things are gathered or to which they tend; an object of attention, action, or force; as, a center of attaction.
Center
The earth.
Center
Those members of a legislative assembly (as in France) who support the existing government. They sit in the middle of the legislative chamber, opposite the presiding officer, between the conservatives or monarchists, who sit on the right of the speaker, and the radicals or advanced republicans who occupy the seats on his left, See Right, and Left.
Center
A temporary structure upon which the materials of a vault or arch are supported in position until the work becomes self-supporting.
Center
One of the two conical steel pins, in a lathe, etc., upon which the work is held, and about which it revolves.
Center
To be placed in a center; to be central.
Center
To be collected to a point; to be concentrated; to rest on, or gather about, as a center.
Where there is no visible truth wherein to center, error is as wide as men's fancies.
Our hopes must center in ourselves alone.
Center
To place or fix in the center or on a central point.
Center
To collect to a point; to concentrate.
Thy joys are centered all in me alone.
Center
To form a recess or indentation for the reception of a center.
Center
An area that is approximately central within some larger region;
It is in the center of town
They ran forward into the heart of the struggle
They were in the eye of the storm
Center
The piece of ground in the outfield directly ahead of the catcher;
He hit the ball to deep center
Center
A building dedicated to a particular activity;
They were raising money to build a new center for research
Center
A point equidistant from the ends of a line or the extremities of a figure
Center
The choicest or most essential or most vital part of some idea or experience;
The gist of the prosecutor's argument
The heart and soul of the Republican Party
The nub of the story
Center
The object upon which interest and attention focuses;
His stories made him the center of the party
Center
A cluster of nerve cells governing a specific bodily process;
In most people the speech center is in the left hemisphere
Center
The middle of a military or naval formation;
They had to reinforce the center
Center
(basketball) the person who plays center on a basketball team
Center
(football) the person who plays center on the line of scrimmage and snaps the ball to the quarterback;
The center fumbled the handoff
Center
A place where some particular activity is concentrated;
They received messages from several centers
Center
Politically moderate persons; centrists
Center
(ice hockey) the person who plays center on a hockey team
Center
The sweet central portion of a piece of candy that is enclosed in chocolate or some other covering
Center
Mercantile establishment consisting of a carefully landscaped complex of shops representing leading merchandisers; usually includes restaurants and a convenient parking area; a modern version of the traditional marketplace;
A good plaza should have a movie house
They spent their weekends at the local malls
Center
The position on a hockey team of the player who participates in the face off at the beginning of the game
Center
The position of the player on the line of scrimmage who puts the ball in play;
It is a center's responsibility to get the football to the quarterback
Center
A position on a basketball team of the player who participates in the center jump to start the game
Center
Center upon;
Her entire attention centered on her children
Our day revolved around our work
Center
Direct one's attention on something;
Please focus on your studies and not on your hobbies
Center
Move into the center;
That vase in the picture is not centered
Center
Equally distant from the extremes
Center
Of or belonging to the political or intellectual right
Center
In social contexts, the center refers to the focal point of activity.
The community center is where everyone meets.
Center
The center in basketball is a player’s position.
Their center dominated the game last night.
Common Curiosities
Is the centroid always at the center of an object?
No, the centroid is at the center only for symmetric, uniform shapes.
Is the center of a sphere the same as its centroid?
Yes, if the sphere is of uniform density.
Does the centroid change with size?
No, the centroid's relative position remains constant despite size changes.
Can a shape have more than one centroid?
No, a single, continuous shape will have only one centroid.
Can you find the centroid of an irregular shape?
Yes, but it requires calculus or experimental methods.
Are the center and centroid the same in a uniform square?
Yes, because the square is symmetrical and uniform.
How do you find the center of a circle?
It’s the point equidistant from all points on the circumference.
Is the center point always clear to identify?
In symmetrical objects, yes; in complex shapes, not necessarily.
Can an object’s center be outside of the object itself?
Yes, like in the case of a ring or a hollow circle.
How is the center used in everyday life?
It can refer to a point of focus, like a town center or a meeting center.
Is the centroid affected by the object's density?
The centroid itself is not, but the center of mass is.
Does the center refer only to physical objects?
No, it can also refer to the focus of attention or activity.
In which industries is knowing the centroid important?
In industries like civil engineering, aerospace, and robotics.
Does the centroid have to be inside the object?
Yes, the centroid of a simple, closed figure is always inside it.
Can the centroid and center coincide in composite shapes?
Not usually, because composite shapes can have non-uniform distribution.
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Written 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.
