Centroid of a Triangle Calculator
Enter the three vertex coordinates of a triangle to compute its centroid G — the point where all three medians meet, located one-third of the way from each side to the opposite vertex. Also shows side lengths, area, and median lengths.
x-coordinate of centroid G — one-third of the way from each side to the opposite vertex
- 1
Sum of x-coordinates
0 + 6 + 3 = 9 - 2
Centroid x̄ = (x₁ + x₂ + x₃) ÷ 3
9 ÷ 3 = 3
How does this calculator work?
The centroid G of a triangle with vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃) is G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). It is the intersection of the three medians, always lies inside the triangle, and is the physical balance point of a uniform triangular plate.
Formula
How this is calculated
The centroid of a triangle is the intersection of its three medians (each median connects a vertex to the midpoint of the opposite side). It always lies inside the triangle and divides each median in the ratio 2:1 from vertex to midpoint — so the centroid is two-thirds of the way from each vertex to the opposite midpoint.
The formula is simple: average the three x-coordinates for Gₓ and average the three y-coordinates for Gᵧ. The result G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3) is exact for any non-degenerate triangle — acute, right-angled, obtuse, scalene, isosceles or equilateral. Collinear points (zero area) are rejected because they form no triangle.
The calculator also reports side lengths (using the distance formula), triangle area (via the shoelace formula), and the three median lengths. In physics, the centroid is where a uniformly dense triangular plate balances on a pin. For the displayed diagram, side labels are proportional to the computed side lengths, and the centroid label G appears at the approximate geometric centre.
Frequently asked questions
Yes. Unlike the circumcentre or orthocentre, the centroid always lies strictly inside the triangle, regardless of whether it is acute, right-angled or obtuse.
The centroid divides each median in the ratio 2:1, measured from the vertex. So the centroid is exactly two-thirds of the way from each vertex to the midpoint of the opposite side.
The centroid (median intersection) is the balance point. The circumcentre is equidistant from all three vertices. The incentre is equidistant from all three sides. All three coincide only in an equilateral triangle.
Also known as
TG we-Calculate Editorial Team. (2026). Centroid of a Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/centroid-of-a-triangle-calculator
TG we-Calculate Editorial Team. "Centroid of a Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/centroid-of-a-triangle-calculator.
TG we-Calculate Editorial Team, "Centroid of a Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/centroid-of-a-triangle-calculator
@misc{wecalculate_centroid_of_a_triangle_calculator, title = {Centroid of a Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/centroid-of-a-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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