How to Find the Centroid of a Triangle Calculator

Centroid Formula:

\[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

Vertex 1 X-coordinate (x₁):

Vertex 1 Y-coordinate (y₁):

Vertex 2 X-coordinate (x₂):

Vertex 2 Y-coordinate (y₂):

Vertex 3 X-coordinate (x₃):

Vertex 3 Y-coordinate (y₃):

Centroid Coordinates (G):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Centroid of a Triangle?

The centroid of a triangle is the point where the three medians of the triangle intersect. It's the "average" of all three vertices' coordinates and represents the triangle's center of mass if it were made of a uniform material.

2. How Does the Calculator Work?

The calculator uses the centroid formula:

\[ G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

Where:

\( G \) — Centroid coordinates (length units)
\( x_1, y_1 \) — Coordinates of first vertex (length units)
\( x_2, y_2 \) — Coordinates of second vertex (length units)
\( x_3, y_3 \) — Coordinates of third vertex (length units)

Explanation: The centroid coordinates are simply the arithmetic mean of all three vertices' x-coordinates and y-coordinates.

3. Importance of Centroid Calculation

Details: The centroid is important in physics for calculating center of mass, in engineering for structural analysis, and in computer graphics for transformations.

4. Using the Calculator

Tips: Enter the coordinates of all three vertices of your triangle. The calculator works with any valid coordinates, whether positive or negative.

5. Frequently Asked Questions (FAQ)

Q1: Is the centroid always inside the triangle?
A: Yes, the centroid is always located inside the triangle, unlike other centers like the circumcenter which may lie outside.

Q2: How does centroid differ from orthocenter?
A: The centroid is the intersection of medians, while the orthocenter is the intersection of altitudes. They coincide only in equilateral triangles.

Q3: Can this calculator work for 3D triangles?
A: No, this is for 2D triangles only. For 3D, you would need to include z-coordinates in the calculation.

Q4: What units should I use?
A: Any consistent units can be used (cm, inches, etc.), just ensure all coordinates use the same units.

Q5: Does the triangle need to be regular?
A: No, the formula works for any triangle shape - scalene, isosceles, or equilateral.