Triangle Centroid Calculator

About Triangle Centroid Calculator

The centroid is the intersection of medians, the average of all three vertices. It is the center of mass for a uniform triangle.

How to use this calculator

1. Enter the coordinates of the triangle's three vertices.
2. Check that each vertex is written as an x value and a y value.
3. Click calculate to find the centroid.
4. Read the centroid as an ordered pair of coordinates.

The formula explained

• \(x_1\) = x-coordinate of the first vertex
• \(y_1\) = y-coordinate of the first vertex
• \(x_2\) = x-coordinate of the second vertex
• \(y_2\) = y-coordinate of the second vertex
• \(x_3\) = x-coordinate of the third vertex
• \(y_3\) = y-coordinate of the third vertex

Step by step method

1. Identify the three vertices of the triangle and write each one as an ordered pair.
2. Add the three x-coordinates together and divide the total by 3.
3. Add the three y-coordinates together and divide the total by 3.
4. Combine the two averages to get the centroid coordinates.

Worked example

Suppose a triangle has vertices at A(2, 4), B(8, 1), and C(5, 7).

1. Find the average x-coordinate: \((2 + 8 + 5) / 3 = 15 / 3 = 5\).
2. Find the average y-coordinate: \((4 + 1 + 7) / 3 = 12 / 3 = 4\).

Tips and common mistakes

• Use the coordinates of all three vertices, not the side lengths.
• Keep x-values with x-values and y-values with y-values.
• If the triangle is drawn on a graph, the centroid should sit at the balance point where the medians meet.
• Double-check signs for negative coordinates before calculating.

Frequently asked questions