Centroid of a Triangle Calculator

How to calculate Centroid of triangle calculator?

The centroid is the intersection of the triangle's medians; its coordinates are the arithmetic mean of the vertices' coordinates.

Formula: (x_centroid, y_centroid) = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)

Using the Centroid of triangle calculator calculator: an example

Example vertices: A(0, 0), B(6, 0), C(0, 3).

Step-by-step calculation:

• Sum x-coordinates: 0 + 6 + 0 = 6.
• Sum y-coordinates: 0 + 0 + 3 = 3.
• Divide each sum by 3: x_centroid = 6 / 3 = 2, y_centroid = 3 / 3 = 1.
• Result: the centroid is at (2, 1).

Frequently Asked Questions

What does the centroid represent?

The centroid is the triangle's center of mass for uniform density and is the common intersection of its medians.

How is centroid different from circumcenter?

The centroid is the average of vertex coordinates and always lies inside the triangle; the circumcenter is the intersection of perpendicular bisectors and can lie outside for obtuse triangles.

Can the centroid lie outside the triangle?

No. For any non-degenerate triangle, the centroid always lies strictly inside the triangle.