🔺 Tetrahedron Volume Calculator
Calculate the volume of a regular tetrahedron
How to Use This Calculator
Enter Edge Length
Input the length of one edge of the regular tetrahedron. Since all edges are equal in a regular tetrahedron, you only need one value.
Click Calculate
Press the "Calculate Volume" button to compute the volume using the formula V = a³/(6√2).
Review Result
View the calculated volume displayed in cubic units. The result includes the step-by-step calculation showing how the formula was applied.
Formula
Volume = a³ / (6√2)
Where a is the edge length of the regular tetrahedron
Where:
- a = edge length (all edges are equal in a regular tetrahedron)
- Volume = space inside the tetrahedron
- √2 ≈ 1.41421
Note: This formula applies only to regular tetrahedra (all edges equal, all faces equilateral triangles). For irregular tetrahedra, use the scalar triple product or other methods.
Example 1: Regular tetrahedron with edge length 6 units
Volume = 6³ / (6√2) = 216 / (6√2)
Volume = 36 / √2 = 36√2 / 2 ≈ 25.46 units³
Example 2: Regular tetrahedron with edge length 10 units
Volume = 10³ / (6√2) = 1000 / (6√2)
Volume = 1000 / (6 × 1.414) ≈ 117.85 units³
Example 3: Regular tetrahedron with edge length 4 units
Volume = 4³ / (6√2) = 64 / (6√2)
Volume ≈ 7.54 units³
About Tetrahedron Volume Calculator
A tetrahedron is a polyhedron with four triangular faces, six edges, and four vertices. A regular tetrahedron has all edges equal and all faces equilateral triangles. This calculator finds the volume of a regular tetrahedron from its edge length using the formula V = a³/(6√2).
When to Use This Calculator
- Geometry: Calculate volumes of tetrahedral shapes in mathematical problems
- Crystallography: Determine volumes in crystal structures with tetrahedral geometry
- Chemistry: Calculate volumes for molecules with tetrahedral arrangements
- 3D Modeling: Work with tetrahedral meshes or structures
- Mathematics Education: Teach students about 3D geometry and tetrahedra
- Engineering: Design tetrahedral frameworks or structures
Why Use Our Calculator?
- ✅ Simple Input: Just enter the edge length
- ✅ Instant Results: Get accurate volume calculations immediately
- ✅ Step-by-Step Display: See the formula applied with your value
- ✅ 100% Accurate: Uses precise mathematical formula
- ✅ Educational: Helps understand tetrahedron geometry
- ✅ Completely Free: No registration required
Understanding Tetrahedra
A regular tetrahedron is the simplest polyhedron:
- 4 Faces: All equilateral triangles
- 6 Edges: All edges have equal length
- 4 Vertices: Four corners where edges meet
- Symmetry: High symmetry - can be rotated to match itself in many ways
- Volume Formula: V = a³/(6√2) for regular tetrahedra
- Relationship to Cube: A regular tetrahedron can be inscribed in a cube
Real-World Applications
Chemistry: Methane (CHâ‚„) has a tetrahedral molecular geometry with carbon at the center. Understanding tetrahedron volume helps in molecular modeling and packing calculations.
Crystallography: Some crystal structures form tetrahedral arrangements. Calculating tetrahedron volumes helps understand crystal densities and atomic packing.
3D Graphics: Tetrahedra are used in 3D meshing and finite element analysis. Regular tetrahedra volumes are essential for computational geometry applications.
Frequently Asked Questions
What is a tetrahedron?
A tetrahedron is a 3D shape with four triangular faces, six edges, and four vertices. A regular tetrahedron has all edges equal and all faces equilateral triangles. It's the simplest polyhedron and a type of pyramid with a triangular base.
Why is the formula a³/(6√2)?
This formula comes from the geometry of a regular tetrahedron. The volume can be derived using coordinate geometry or by relating it to a cube. The factor 6√2 appears from the specific geometry of equilateral triangles meeting at vertices.
Does this work for irregular tetrahedra?
No, this formula is specifically for regular tetrahedra (all edges equal). For irregular tetrahedra, use the scalar triple product: V = |(a × b) · c| / 6, where a, b, c are vectors from one vertex to the other three vertices.
How is a tetrahedron different from a pyramid?
A tetrahedron is a type of pyramid - specifically a triangular pyramid. It has a triangular base and three triangular faces meeting at an apex. "Tetrahedron" emphasizes that it has four faces, while "triangular pyramid" emphasizes the pyramid structure.
What's the relationship between tetrahedron and cube volume?
A regular tetrahedron can be inscribed in a cube. The tetrahedron's volume is 1/3 of the cube's volume. If a cube has edge length a, a tetrahedron inscribed in it has volume a³/3 (different from the formula for a tetrahedron with edge a, which is a³/(6√2)).
Can I calculate surface area too?
Yes! For a regular tetrahedron with edge length a, surface area = 4 × (area of one equilateral triangle) = 4 × (a²√3/4) = a²√3. The calculator focuses on volume, but surface area can be calculated separately.