Tetrahedron Volume Calculator

The volume of a regular tetrahedron with edge length a is V = a³√2/12. This can also be written as V = a³/(6√2).

If you know the height h, use V = h³/(6√3). For a regular tetrahedron, the height h = a√(2/3), so you can convert between edge length and height.

A regular tetrahedron is a polyhedron with four equilateral triangle faces, six equal edges, and four vertices. It is one of the five Platonic solids.

A tetrahedron has a triangular base and three triangular faces meeting at an apex. A pyramid can have any polygon as its base. A tetrahedron is a specific type of triangular pyramid.

Yes, for an irregular tetrahedron with known vertex coordinates, use the scalar triple product formula: V = |(a-d)·((b-d)×(c-d))|/6.

For a regular tetrahedron, the height h = a√(2/3) ≈ 0.8165a, where a is the edge length.

If you know the circumradius R (distance from center to vertex), use V = 8R³/(3√6).

The surface area is SA = a²√3, where a is the edge length. This comes from four equilateral triangle faces, each with area a²√3/4.

A tetrahedron has 4 faces (all triangles), 6 edges, and 4 vertices. It satisfies Euler's formula: V - E + F = 2 (4 - 6 + 4 = 2).

Tetrahedron volume is used in molecular chemistry (methane is tetrahedral), computer graphics (tetrahedral meshing), finite element analysis, and structural engineering.

A regular tetrahedron with edge length a can be inscribed in a cube. The tetrahedron occupies 1/3 of the cube's volume.

Yes, the tetrahedron is the simplest convex polyhedron, requiring the minimum number of faces (4) to enclose a 3D volume.

This calculator uses high-precision floating-point arithmetic and provides results accurate to multiple decimal places. For most practical purposes, the results are exact.

Yes, if the triangular pyramid is regular (all edges equal), the formulas are the same. For non-regular triangular pyramids, you need the base area and height.

The inradius (radius of the inscribed sphere) is r = a√6/12 ≈ 0.2041a. It is the distance from the center to any face.

To convert volume from one cubic unit to another, multiply by the appropriate conversion factor. For example, cm³ to m³: multiply by 0.000001 (10⁻⁶).

The center of mass (centroid) of a regular tetrahedron is located at 1/4 of the height from the base, or equidistant from all four vertices.

A disphenoid has congruent isosceles triangle faces. For volume, you need either edge lengths and dihedral angle, or vertex coordinates. Use the general formula V = |det([b-a, c-a, d-a])|/6.

The dihedral angle (angle between two adjacent faces) is arccos(1/3) ≈ 70.53°. This is a fixed property of all regular tetrahedra.

The tetrahedron is the 3-simplex. In n dimensions, the n-simplex has n+1 vertices. The volume formula generalizes using determinants of edge vectors.

The Tetrahedron Volume Calculator uses standard mathematical formulas validated against authoritative references. The specific formula is displayed in the calculator interface with a detailed explanation of each variable.

Each calculator includes a step-by-step worked example showing exactly how the formula is applied. You can follow these steps with pen and paper to verify any result.

The Tetrahedron Volume Calculator accepts numeric inputs including integers and decimals. Invalid inputs (letters, special characters) are rejected with clear error messages.