Centroid of a Triangle Calculator

In geometry, the centroid (often denoted as G) is defined as the arithmetic mean of the coordinates of a triangle's three vertices. If you have a triangle with vertices defined by coordinates (X1, Y1), (X2, Y2), and (X3, Y3), the centroid coordinates (Xc, Yc) are computed using simple averaging formulas. To find the X-coordinate, sum all three X-values and divide by three: Xc = (X1 + X2 + X3) / 3. Similarly, to find the Y-coordinate, sum all three Y-values and divide by three: Yc = (Y1 + Y2 + Y3) / 3. This straightforward arithmetic works because the centroid represents the center of mass for a uniform triangular lamina.

Consider a triangle plotted on a coordinate plane with vertex A at (1, 2), vertex B at (5, 6), and vertex C at (9, 4). To find the centroid manually, we first plug the X-coordinates into our formula: Xc = (1 + 5 + 9) / 3. Summing the numerator gives 15, and 15 divided by 3 yields an Xc value of 5. Next, we calculate the Y-coordinate by averaging the Y-values: Yc = (2 + 6 + 4) / 3. Summing these gives 12, and 12 divided by 3 yields a Yc value of 4. Therefore, the exact centroid of this triangle is located at the coordinate point (5, 4).

When plotting your points, always double-check that you are using a consistent Cartesian coordinate system with correct positive and negative signs. A common pitfall is accidentally swapping the X and Y inputs when transferring data from a technical drawing into the calculator fields. Additionally, remember that the centroid always lies strictly inside the triangle, regardless of whether the shape is acute, obtuse, or right-angled, making it a reliable reference point for structural balancing.