Centroid Calculator
Centroid Coordinates: -
Area: -
Understanding the Centroid
What is a Centroid?
The centroid of a triangle is a special point where all three medians intersect. Key characteristics include:
- Also known as the center of mass or geometric center
- Located at ⅔ distance from any vertex to the midpoint of the opposite side
- Divides each median in the ratio 2:1
- Independent of the triangle's orientation
- Always located inside the triangle
Centroid Formulas
Coordinate Formulas
x = (x₁ + x₂ + x₃)/3
y = (y₁ + y₂ + y₃)/3
Distance from Vertex
Distance = ⅔ × median length
Properties of Centroid
Barycentric Coordinates
(1:1:1)
Center of Mass
Balance point of triangle
Median Intersection
Intersection of all three medians
Area Division
Divides triangle into six equal areas
Advanced Properties
Euler's Theorem
The centroid lies on the Euler line, between the orthocenter and circumcenter
Distance Ratio
The centroid divides the distance between the circumcenter and orthocenter in ratio 2:1
Moment of Inertia
Minimizes the mean square distance to all points in the triangle
Real-World Applications
Physics
Used in calculating center of mass and balance points
Engineering
Critical in structural design and stability analysis
Computer Graphics
Essential for 3D modeling and animation pivot points
Robotics
Used in motion planning and stability calculations