Centroid Calculator

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Find the centroid (geometric center) of a triangle given its three vertices.

Vertex 1 (A)

Vertex 2 (B)

Vertex 3 (C)

Centroid Coordinates

G(x)1.0000

G(y)1.3333

Coordinate(1, 1.33)

About this calculator

What is a Centroid?

The centroid of a triangle is the point where its three medians intersect. A median is a line segment drawn from a vertex to the midpoint of the opposite side. Physically, the centroid is the center of mass of a thin plate (lamina) uniform in density with the same shape as the triangle.

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Pro Tips

The centroid always lies inside the triangle.
It divides each median in a 2:1 ratio (distance from vertex to centroid is 2x distance from centered to opposite side midpoint).
This simple averaging formula works for any polygon's vertex centroid, though the center of area might differ for non-triangles.

Fun Facts

"If you cut a triangle out of cardboard, you can balance it perfectly on the tip of a pencil at its centroid."
"The centroid is one of the four centers of a triangle, along with the circumcenter, incenter, and orthocenter."
"For an equilateral triangle, all four centers are the exact same point."

Formula: Gx = (x₁ + x₂ + x₃) / 3, Gy = (y₁ + y₂ + y₃) / 3