GeomBench

Centroid Calculator

Average the corners, find the balance point.

x₁

y₁

x₂

y₂

x₃

y₃

Centroid x

G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)

Centroid y: 2

What you entered

x₁: 0y₁: 0x₂: 6y₂: 0x₃: 3y₃: 6

1
Centroid x = (x₁ + x₂ + x₃) ÷ 3
(0 + 6 + 3) ÷ 3= 3
2
Centroid y = (y₁ + y₂ + y₃) ÷ 3
(0 + 0 + 6) ÷ 3= 2

Result

Centroid x: 3

The centroid of the triangle with vertices (0, 0), (6, 0), (3, 6) is (3, 2).

Centroid of a triangle from its three vertices

The centroid is simply the average of the three x coordinates and the average of the three y coordinates.

Vertex 1	Vertex 2	Vertex 3	Centroid
(0, 0)	(6, 0)	(0, 6)	(2.0000, 2.0000)
(1, 1)	(5, 1)	(3, 7)	(3.0000, 3.0000)
(0, 0)	(4, 0)	(2, 5)	(2.0000, 1.6667)
(-3, 0)	(3, 0)	(0, 4)	(0.0000, 1.3333)
(2, 2)	(8, 2)	(5, 8)	(5.0000, 4.0000)

The centroid is the triangle's centre of mass, so a uniform triangular plate balances on a pin placed exactly there. It always sits inside the triangle, unlike the circumcentre which can fall outside an obtuse one. Geometrically it is where the three medians meet, and it divides each median in a 2:1 ratio measured from the vertex - the last two rows show the y coordinate sitting one third of the way up from the base, at 1.3333 of a height of 4 and 4.0000 of a height reaching 8.

Just the average of the three corners

The centroid's coordinates are simply the mean of the three vertices' x-values and the mean of their y-values — no angles or side lengths needed, just averaging.

Where a triangle actually balances

The centroid is the triangle's true center of mass — if cut from uniform material, it would balance perfectly on a pin placed exactly at this point, and it's also where all three medians (vertex-to-opposite-midpoint lines) intersect.

Frequently asked questions

How do I find the centroid of a triangle?

Centroid = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). Just average all three x-coordinates and all three y-coordinates. For vertices (0,0), (6,0), (3,9): centroid = (3, 3).

What is the difference between centroid, incenter, and circumcenter?

Centroid: intersection of medians, the balance point (always inside). Incenter: intersection of angle bisectors, center of the inscribed circle (always inside). Circumcenter: intersection of perpendicular bisectors, center of the circumscribed circle (can be outside for obtuse triangles).

Where does the centroid divide each median?

The centroid divides each median in a 2:1 ratio from vertex to opposite midpoint. It's always located ⅓ of the way from each side and ⅔ of the way from each vertex.