Centroid of a Triangle Calculator
Find the centroid (center of mass) of a triangle using vertex coordinates
Calculate Triangle Centroid
First vertex of the triangle
Second vertex of the triangle
Third vertex of the triangle
Centroid Results
Enter three non-collinear points to calculate the centroid
Example Calculation
Triangle with vertices:
Point A: (1, 1)
Point B: (3, 4)
Point C: (4, 5)
Centroid Calculation
xc = (1 + 3 + 4) / 3 = 8 / 3 = 2.667
yc = (1 + 4 + 5) / 3 = 10 / 3 = 3.333
Centroid: (2.667, 3.333)
Triangle Centers
Centroid
Center of mass
Intersection of medians
Circumcenter
Center of circumcircle
Intersection of perpendicular bisectors
Incenter
Center of incircle
Intersection of angle bisectors
Orthocenter
Meeting point of altitudes
Intersection of altitudes
Centroid Properties
The centroid is the center of mass for uniform density
It divides each median in a 2:1 ratio
Located at ⅓ distance from each side
Always lies inside the triangle
Balancing point of the triangle
Understanding the Centroid of a Triangle
What is a Centroid?
The centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment joining a vertex to the midpoint of the opposite side. The centroid is also known as the center of mass or center of gravity of the triangle.
Key Properties
- •The centroid divides each median in a 2:1 ratio
- •It's located ⅔ of the way from each vertex to the opposite side
- •The centroid always lies inside the triangle
- •It's the balance point for a uniform triangular object
Centroid Formula
G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
Where G is the centroid and (x₁,y₁), (x₂,y₂), (x₃,y₃) are the vertices
Step-by-Step Calculation
- 1. Add all x-coordinates: x₁ + x₂ + x₃
- 2. Divide by 3 to get x-coordinate of centroid
- 3. Add all y-coordinates: y₁ + y₂ + y₃
- 4. Divide by 3 to get y-coordinate of centroid
Note: The centroid is simply the arithmetic mean of the three vertices' coordinates.
Applications of the Centroid
Engineering
Structural analysis, center of mass calculations for triangular components
Computer Graphics
Triangle mesh processing, 3D modeling, and geometric transformations
Navigation
Geographic center calculations, triangulation methods