Tetrahedron Volume Calculator
Calculate volume, surface area, height, and sphere properties of tetrahedrons
Calculate Tetrahedron Volume
Length of each edge in a regular tetrahedron
Results
Sphere Properties
SA:V Ratio: 0.000000 m⁻¹
Properties: Regular tetrahedron with 4 triangular faces, 6 edges, and 4 vertices
Example Calculation
Regular Tetrahedron Example
Given: Regular tetrahedron with edge length L = 8 cm
Volume: V = L³/(6√2) = 8³/(6√2) = 512/8.485 ≈ 60.34 cm³
Height: H = (√6/3) × L = (√6/3) × 8 ≈ 6.53 cm
Surface Area: A = √3 × L² = √3 × 64 ≈ 110.85 cm²
Sphere Calculations
• Insphere radius: r_i = L/(2√6) = 8/(2√6) ≈ 1.63 cm
• Midsphere radius: r_k = L/(2√2) = 8/(2√2) ≈ 2.83 cm
• Circumsphere radius: r_u = (√6/4) × L = (√6/4) × 8 ≈ 4.90 cm
Tetrahedron Properties
Triangular faces
Edges
Vertices
Types of spheres
Key Formulas
Volume
V = L³/(6√2)
Height
H = (√6/3) × L
Surface Area
A = √3 × L²
Insphere
r_i = L/(2√6)
Circumsphere
r_u = (√6/4) × L
L = Edge length
Understanding Tetrahedrons
What is a Tetrahedron?
A tetrahedron is the simplest 3D polyhedron, consisting of four triangular faces. It's also known as a triangular pyramid. In a regular tetrahedron, all faces are equilateral triangles and all edges have the same length.
Calculation Methods
- •Edge Length: For regular tetrahedrons
- •Base & Height: For any tetrahedron
- •Coordinates: Using 4 vertex coordinates
Sphere Types
Insphere
Largest sphere inside, touching all faces
Midsphere
Sphere touching all edges at midpoints
Circumsphere
Sphere passing through all vertices
Applications: Computer simulations, molecular chemistry, ancient gaming dice, and architectural structures.