Enter the coordinates of your triangle's three vertices — Point A (x₁, y₁), Point B (x₂, y₂), and Point C (x₃, y₃) — and the Triangle Centroid Calculator finds the exact centroid coordinates (Cx, Cy). The centroid is the geometric center and center of gravity of any triangle, calculated as the average of all three vertex coordinates.
Centroid X Coordinate
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Centroid Y Coordinate
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Centroid Point (Cx, Cy)
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Triangle Area
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Triangle Perimeter
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The centroid of a triangle is the point where all three medians of the triangle intersect. A median connects a vertex to the midpoint of the opposite side. The centroid is also the triangle's center of gravity, meaning if you cut the triangle out of a uniform material, it would balance perfectly on the centroid point.
To find the centroid, average the x-coordinates of all three vertices and average the y-coordinates separately. The formula is: Cx = (x₁ + x₂ + x₃) / 3 and Cy = (y₁ + y₂ + y₃) / 3. This gives you the (Cx, Cy) coordinates of the centroid.
The centroid divides each median in a ratio of 2:1 from the vertex to the midpoint of the opposite side. This means the centroid is always located two-thirds of the way from any vertex to the midpoint of the opposite side, and one-third of the way from that midpoint back to the vertex.
No. Unlike the orthocenter or circumcenter, the centroid of a triangle always lies inside the triangle, regardless of whether the triangle is acute, obtuse, or right-angled. This is because it is the arithmetic mean of the three vertex positions.
The centroid is where the medians meet and represents the center of mass. The circumcenter is equidistant from all three vertices and is the center of the circumscribed circle. The incenter is equidistant from all three sides and is the center of the inscribed circle. All three are different special points within (or potentially outside) a triangle.
Yes. The centroid formula Cx = (x₁ + x₂ + x₃) / 3 and Cy = (y₁ + y₂ + y₃) / 3 works universally for equilateral, isosceles, scalene, right, acute, and obtuse triangles. Any valid set of three non-collinear points will produce a meaningful centroid.
If the three points lie on a straight line, they do not form a triangle — the area would be zero. In this case, the centroid formula still produces a coordinate point (the average of the three points), but it lies on the same line and does not represent a meaningful geometric centroid of a 2D triangle.
Yes. The centroid formula works with any real number coordinates, including negative values. Simply enter the x and y values for each vertex — positive, negative, or zero — and the calculator will correctly compute the centroid location in the coordinate plane.