What Is a Centroid Calculator?
A centroid calculator finds the centroid — the geometric center, or center of mass — of a triangle from the coordinates of its three vertices. The centroid is the point where the triangle would balance, and it is found by averaging the vertex coordinates. Enter the three vertices and the calculator returns the centroid's coordinates.
How to Use the Calculator
- Enter the three vertices of the triangle as (x, y) coordinate pairs.
- Calculate — see the centroid coordinates.
The Centroid Formula
The centroid is the average of the three vertices' coordinates:
Centroid = ((x₁ + x₂ + x₃) ÷ 3, (y₁ + y₂ + y₃) ÷ 3)
For vertices (0, 0), (6, 0), and (0, 9): the centroid is ((0 + 6 + 0) ÷ 3, (0 + 0 + 9) ÷ 3) = (2, 3).
What the Centroid Represents
| Property | Description |
|---|---|
| Balance point | The triangle balances perfectly on its centroid |
| Median intersection | All three medians meet at the centroid |
| 2:1 ratio | The centroid divides each median 2:1 from the vertex |
Centroid and Medians
A median connects a vertex to the midpoint of the opposite side. All three medians of a triangle intersect at a single point — the centroid — which divides each median so the segment from the vertex is twice the length of the segment to the midpoint.
Where Centroids Are Used
- Engineering: finding the center of mass of shapes.
- Geometry: a key triangle center alongside the incenter and circumcenter.
- Graphics and design: balancing and positioning shapes.
Frequently Asked Questions
What is the centroid of a triangle?
The centroid is the geometric center of a triangle — the point where it balances and where its three medians intersect.
How do you find the centroid?
Average the x-coordinates and the y-coordinates of the three vertices separately: centroid = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).
What is the 2:1 ratio of the centroid?
The centroid divides each median so that the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side.
Is the centroid the same as the center of mass?
For a triangle of uniform density, yes — the centroid is the center of mass, the balance point of the shape.
Is this centroid calculator free?
Yes — it is completely free, requires no signup, and finds the triangle's center.