Regular Tetrahedron Calculator
Tetrahedron Volume and Surface Area Calculator
Calculate the volume and surface area of a tetrahedron with our easy-to-use calculator. Learn about tetrahedron formulas, applications, and explore interactive examples.
A tetrahedron is a three-dimensional shape with four triangular faces, six edges, and four vertices. It's the simplest possible regular polyhedron and appears frequently in nature, chemistry, and engineering applications.
Formula
Volume = (a³)/(6√2)
Surface Area = a²√3
Where:
- a:length of one edge (all edges are equal in a regular tetrahedron)
How to Calculate Tetrahedron Volume
The volume of a regular tetrahedron is calculated using the cube of its edge length (a³) divided by 6√2. This formula comes from the geometric properties of the shape and its regular triangular faces.
Understanding Surface Area
The surface area is calculated by finding the area of all four triangular faces. For a regular tetrahedron, this equals the square of the edge length multiplied by √3. Each face is an equilateral triangle.
Real-World Applications
Tetrahedra are found in molecular structures (like methane CH₄), crystal formations, architectural designs, and engineering. They're also used in 3D modeling and computer graphics for their structural stability.
Frequently Asked Questions
What makes a tetrahedron regular?
A regular tetrahedron has all faces as identical equilateral triangles and all edges of equal length. All face angles and dihedral angles (angles between faces) are also equal.
How is a tetrahedron different from a pyramid?
While both have triangular faces, a regular tetrahedron has four identical equilateral triangular faces. A typical pyramid has a square base and four triangular faces, with only the triangular faces being identical.
Where are tetrahedra used in the real world?
Tetrahedra appear in molecular structures (like methane), crystal lattices, architectural designs, and engineering structures. They're also used in finite element analysis and computer graphics.