Tetrahedron Centroid Calculator

Vertex 1 (A):

Vertex 2 (B):

Vertex 3 (C):

Vertex 4 (D):

Centroid Coordinates: -

Distance from Origin: -

Understanding Tetrahedron Centroids

What is a Tetrahedron Centroid?

The centroid of a tetrahedron is the arithmetic mean position of all points in the tetrahedron's volume. It represents the center of mass for a tetrahedron of uniform density.

Centroid Coordinates = (x̄, ȳ, z̄)

where:

x̄ = (x₁ + x₂ + x₃ + x₄)/4
ȳ = (y₁ + y₂ + y₃ + y₄)/4
z̄ = (z₁ + z₂ + z₃ + z₄)/4

Properties of Tetrahedron Centroids

The centroid divides each median in the ratio 3:1
It is the intersection point of all four medians
Located at 1/4 of the way from any face to the opposite vertex
Coincides with the center of mass for uniform density
Minimizes the sum of squared distances to vertices

Advanced Tetrahedron Properties

Medians

Lines connecting vertices to face centroids

Volume Formula

V = |det(v₂-v₁, v₃-v₁, v₄-v₁)|/6

Face Centroids

Average of three vertices

Moment of Inertia

Depends on mass distribution

Applications and Significance

Structural Engineering: Center of mass calculations
Computer Graphics: 3D modeling and animation
Molecular Geometry: Tetrahedral molecular structures
Crystallography: Crystal structure analysis
Finite Element Analysis: Mesh generation