What does centroid mean?
The centroid is the point at which all the positions of a shape's points average out — its true geometric center of balance. For simple, symmetrical figures like circles, squares, and equilateral triangles, this is exactly where intuition places the middle, but for irregular shapes the centroid can fall anywhere, even outside the boundary of the object itself. In physics, when a body has uniform density, its centroid coincides with its center of mass, making it essential to structural engineering, mechanics, and robotics. The term also extends into modern computing: machine-learning algorithms such as k-means clustering repeatedly compute centroids of data groups to organize information. Precise yet intuitive, the centroid captures the idea that every collection of points has a single representative position — a concept as useful for balancing a steel beam as it is for sorting data.
nounThe point at which the geometric center of a figure, body, or distributed mass is located; the arithmetic mean position of all the points in a shape or set of points. In a uniform body, the centroid coincides with the center of gravity.
- The geometric center — the arithmetic mean position of all points in a plane figure or solid.
- The center of mass (or center of gravity) of a physical body of uniform density.
"The centroid of a triangle lies at the point where its three medians intersect."
"Engineers calculated the centroid of the irregular cross-section to determine where the load should be applied."
"In k-means clustering, each data point is assigned to the cluster whose centroid is nearest."
Standard English plural; commonly used when comparing multiple shapes or cluster centers.
"The algorithm updated all three cluster centroids after each iteration."
A crescent moon's centroid isn't even inside the moon — it floats in empty space beside it.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of centroid
The word "centroid" combines Greek-derived "centr-" from Latin "centrum" (itself borrowed from Greek "kentron," meaning sharp point or center) with the suffix "-oid," from Greek "-oeides," meaning resembling or having the form of. It entered scientific English in the 19th century alongside related terms like "barycenter" as geometry and mechanics formalized their vocabulary. Its root also underlies words such as "concentric," "eccentric," and "heliocentric."
Word family
Usage notes
Centroid is a technical term used chiefly in mathematics, physics, engineering, statistics, and computer science. It carries no emotional connotation and appears almost exclusively in formal or academic registers; everyday speech would simply use "center" or "middle."
Don't confuse with
"Center" refers to the general middle point of an object or area, while "centroid" specifically means the mean position of all points in a shape or mass — which may lie outside the object for irregular figures.