Volume of Tetrahedron Calculator

Calculate the volume of a tetrahedron using different methods with step-by-step solutions

m

Enter Vertex Coordinates

m²
m

Understanding Tetrahedron Volume

Key Concepts

1. Basic Properties

  • Four triangular faces
  • Six edges
  • Four vertices
  • Simplest 3D polyhedron

2. Applications

  • Molecular geometry
  • Crystal structures
  • Finite element analysis
  • Computer graphics

Volume Formulas

Method Formula Variables
Regular Tetrahedron \[ V = \frac{a^3}{6\sqrt{2}} \] a = edge length
Height and Base \[ V = \frac{1}{3}Bh \] B = base area, h = height
Coordinates \[ V = \frac{|\vec{a} \cdot (\vec{b} \times \vec{c})|}{6} \] Vectors from one vertex

Calculation Tips

For accurate volume calculations:

  • Ensure accurate measurements
  • Consider symmetry in regular tetrahedra
  • Verify coordinate positions
  • Check units consistency
  • Use appropriate precision