Standard Lemma guide

centroid

noun · 7 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: engineering, geometry, mathematics, natural-sciences, physical-sciences, physics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

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.

Definition source: English Wiktionary via Wiktextract

Usage: specifically

Topics: geometry, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

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

Definition source: English Wiktionary via Wiktextract

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

4

noun

Meaning 4

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

Examples

  • The centroid of an arbitrary function f is given by #92;frac#123;#92;intxf(x)dx#125;#123;#92;intf(x)dx#125;, where the integrals are calculated over the domain of f.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

5

noun

Meaning 5

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

Definition source: English Wiktionary via Wiktextract

Qualifier: cluster analysis

Topics: mathematics, sciences, statistics

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

6

noun

Meaning 6

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.

Definition source: English Wiktionary via Wiktextract

Topics: graph-theory, mathematics, sciences

Examples

  • 1974 [Prentice-Hall], Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, 2017, Dover, page 248, Just as in the case of centers of a tree (Section 3-4), it can be shown that every tree has either one centroid or two centroids. It can also be shown that if a tree has two centroids, the centroids are adjacent.
  • 2009, Hao Yuan, Patrick Eugster, An Efficient Algorithm for Solving the Dyck-CFL Reachability Problem on Trees, Giuseppe Castagna (editor), Programming Languages and Systems: 18th European Symposium, Proceedings, Springer, LNCS 5502, page 186, A node x in a tree T is called a centroid of T if the removal of x will make the size of each remaining connected component no greater than |T|/2. A tree may have at most two centroids, and if there are two then one must be a neighbor of the other [6, 5]. Throughout this paper, we specify the centroid to be the one whose numbering is lexicographically smaller (i.e., we number the nodes from 1 to n). There exists a linear time algorithm to compute the centroid of a tree due to the work of Goldman [21]. We use operatorname CT(T) to denote the centroid of T computed by the linear time algorithm.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

7

noun

Meaning 7

the center of mass of an object of uniform density

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: center of mass, centre of mass

History

Etymology

From centre + -oid. From 1844, used as a replacement for the older terms "centre of gravity" and "centre of mass" in situations described in purely geometrical terms, and subsequently used for further generalisations.

Across languages

Translations

17 source translations are retained for this English entry.

  • Chinese Mandarin: 形心 (xíngxīn) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Finnish: painopiste — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • French: centroïde — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Ido: centroido — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Irish: meánlár — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Italian: centroide — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Korean: 도심 (dosim) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Korean: 모양중심 (moyangjungsim) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Polish: centroid — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Portuguese: centroide — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Russian: центро́ид (centróid) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Russian: барице́нтр (baricéntr) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Russian: центр тя́жести (centr tjážesti) — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Spanish: centroide — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Vietnamese: trọng tâm — mean position of points in a geometrical figure — see also center of gravity, barycenter
  • Polish: centroid — cluster analysis: arithmetic mean or median of points in a cluster
  • Polish: centroid — graph theory: type of node in a tree
Real reading context

centroid in complete knowledge articles

Incenter Ideas & learning · Advanced · 4 uses