Triangle Centroid Calculator
Find the centroid (geometric centre of mass) of a triangle from its three vertex coordinates — the average of the three points.
How it works
G = ( (x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 )
The centroid is the triangle’s balance point — the place where a uniform triangular plate would balance on a pin. It is simply the average of the three vertex coordinates. Geometrically it is where the three medians (each joining a vertex to the midpoint of the opposite side) cross, and it always divides every median in a 2:1 ratio measured from the vertex.
Worked example
For A(0, 0), B(9, 0) and C(3, 6): Gx = (0 + 9 + 3)/3 = 4 and Gy = (0 + 0 + 6)/3 = 2, so the centroid is at (4, 2).
Sources: Centroid — Wikipedia
Frequently asked questions
Is the centroid always inside the triangle?
Yes. Because it is the average of the three vertices, the centroid always lies strictly inside the triangle, unlike the circumcentre or orthocentre which can fall outside.
What is the 2:1 median property?
Each median is split by the centroid so that the segment from the vertex to the centroid is twice as long as the segment from the centroid to the opposite side’s midpoint.
Is the centroid the same as the incentre or circumcentre?
No. The centroid balances area, the incentre is equidistant from the sides, and the circumcentre is equidistant from the vertices. They coincide only for an equilateral triangle.
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This calculator is for educational purposes. Double-check important results before acting on them.