Centroid Calculator
Calculate the centroid (geometric center) of triangles, polygons, and point sets
Calculate Centroid
Triangle Vertices
Centroid Results
Formula used: Gₓ = (x₁ + x₂ + ... + xₖ) / k, Gᵧ = (y₁ + y₂ + ... + yₖ) / k
Calculation type: Triangle centroid (barycenter)
Example Calculation
Triangle Example
Vertices: A(0, 0), B(0, 3), C(3, 3)
Calculation:
Gₓ = (0 + 0 + 3) / 3 = 1
Gᵧ = (0 + 3 + 3) / 3 = 2
Centroid: (1, 2)
Centroid Properties
Geometric Center
Balance point of the shape
Mean Position
Average of all vertices
Center of Mass
For uniform density objects
Centroid Tips
For triangles, centroid divides medians in 2:1 ratio
In convex shapes, centroid lies inside the shape
For concave shapes, centroid may lie outside
Centroid of points is their arithmetic mean
Understanding Centroids
What is a Centroid?
A centroid, also called a geometric center, is the center of mass of an object of uniform density. It's the point where the object would balance perfectly if placed on a pin tip. For geometric shapes, it represents the average position of all points in the shape.
Applications
- •Engineering: Center of gravity calculations
- •Computer Graphics: Object positioning
- •Statistics: Data clustering (K-means)
- •Architecture: Structural balance points
Calculation Methods
Points & Triangles
Gₓ = (x₁ + x₂ + ... + xₙ) / n
Gᵧ = (y₁ + y₂ + ... + yₙ) / n
Polygons (Shoelace)
Cₓ = (1/6A) Σ(xᵢ + xᵢ₊₁)(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)
Cᵧ = (1/6A) Σ(yᵢ + yᵢ₊₁)(xᵢyᵢ₊₁ - xᵢ₊₁yᵢ)