A tetrahedron is a three-dimensional geometric shape with four triangular faces. A regular tetrahedron has all edges of equal length and all faces as equilateral triangles. This calculator helps you find volume, surface area, height, edge length, and inscribed/circumscribed sphere radii for regular tetrahedrons.
A regular tetrahedron is one of the five Platonic solids, featuring four equilateral triangle faces, four vertices, and six edges of equal length. It's the simplest convex polyhedron and forms a triangular pyramid. The tetrahedron has remarkable symmetry properties and appears frequently in chemistry (molecular geometry), crystallography, and structural engineering. Notable examples include the carbon atom structure in diamond and the shape of certain viral capsids.
Enter a value for any single property of the tetrahedron. The calculator will automatically compute all other properties. You can input edge length, height, volume, surface area, or any of the three sphere radii. Select your preferred units from the dropdown menus. All fields update instantly as you type, showing the relationships between different geometric properties.
Tetrahedron calculations are essential in multiple fields:
Chemistry: Understanding tetrahedral molecular geometry (methane, ammonium ion)
Architecture: Designing space frames and geodesic structures
3D Modeling: Computing mesh properties and collision detection
Education: Teaching solid geometry and spatial reasoning
For a regular tetrahedron with edge length a:
Volume: V = (a³√2) / 12
Surface Area: A = √3 a²
Height: h = (√6 / 3) a
Circumsphere Radius: R = (√6 / 4) a
Midsphere Radius: r = (√2 / 4) a
Insphere Radius: r = (√6 / 12) a
What is the difference between the three sphere radii?
The insphere (inner sphere) fits inside the tetrahedron touching all faces. The midsphere is tangent to all six edges. The circumsphere (outer sphere) passes through all four vertices. Each has a specific geometric relationship to the edge length.
Can I use this for irregular tetrahedrons?
No, this calculator is designed specifically for regular tetrahedrons where all edges are equal length. Irregular tetrahedrons require different formulas based on individual edge lengths and angles.
What is the surface to volume ratio used for?
Surface to volume ratio is important in chemistry and biology for understanding molecular efficiency, heat transfer, and material properties. A higher ratio means more surface area relative to volume, affecting reaction rates and thermal properties.
