Triangle Centroid Calculator
Find the centroid (G) of any triangle from its three vertex coordinates. Also shows median lengths, midpoints, side lengths, and area.
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| Median | From Vertex | Midpoint | Median Length | 2:1 split |
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Frequently Asked Questions
The centroid (G) is the point where the three medians of a triangle intersect. A median connects a vertex to the midpoint of the opposite side. The centroid is the triangle's center of mass — if cut from uniform material, it balances at the centroid. Formula: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).
The centroid G is simply the average of the three vertices: Gx = (x₁ + x₂ + x₃) / 3 and Gy = (y₁ + y₂ + y₃) / 3. For example, triangle (0,0), (6,0), (3,6): Gx = (0+6+3)/3 = 3, Gy = (0+0+6)/3 = 2. So G = (3, 2).
A median connects a vertex to the midpoint of the opposite side. Every triangle has exactly 3 medians, all meeting at the centroid. Length of median from vertex A: m_a = ½√(2b² + 2c² − a²), where a, b, c are side lengths. The centroid divides each median in a 2:1 ratio from vertex to midpoint.
The centroid divides each median in the ratio 2:1 from vertex to midpoint. The distance from a vertex to the centroid is 2/3 of the full median length, and the distance from the centroid to the midpoint of the opposite side is 1/3 of the median's length. This holds for all three medians.
Centroid vs Other Triangle Centers
A triangle has four classical centers: Centroid (G) — intersection of medians (center of mass); Circumcenter (O) — equidistant from all three vertices; Incenter (I) — equidistant from all three sides; Orthocenter (H) — intersection of altitudes. These four points are collinear on the Euler line (except for equilateral triangles where all coincide).
- Centroid always lies inside the triangle
- Centroid divides each median in ratio 2:1 (vertex side is longer)
- The three medians divide the triangle into 6 smaller triangles of equal area
- Centroid coordinates = arithmetic mean of vertex coordinates