Tetrahedron Calculator

A regular tetrahedron is a three-dimensional solid with four equilateral triangular faces, six edges of equal length, and four vertices. It is one of the five Platonic solids, meaning all its faces, edges, and angles are identical.

The volume is calculated using the formula V = a³ / 12 × √2, where a is the edge length. For example, an edge length of 5 units gives a volume of approximately 29.46 cubic units.

The total surface area is A = a² × √3, which sums the areas of all four equilateral triangular faces. Each face has an area of (√3/4) × a².

The circumradius (rc = a/4 × √6) is the radius of the sphere passing through all four vertices. The midradius (rm = a/4 × √2) is the radius of the sphere touching all six edges. The inradius (ri = a/12 × √6) is the radius of the largest sphere that fits inside the tetrahedron.

The height h = a/3 × √6 is the perpendicular distance from any vertex to the opposite face. It is one-third of the square root of six times the edge length.

The A/V ratio indicates how much surface area exists per unit of volume. For a regular tetrahedron, A/V = 6√6 / a. A smaller edge length results in a higher ratio, meaning more surface area relative to volume.

No — this calculator is specifically designed for regular tetrahedrons, where all four faces are equilateral triangles and all six edges are equal. For irregular tetrahedrons with different edge lengths or vertex coordinates, a general tetrahedron calculator would be needed.

The calculator works with any consistent unit of length (meters, centimeters, inches, etc.). Edge length, height, and radii share the same unit; surface area is in that unit squared; volume is in that unit cubed; and the A/V ratio is in that unit to the power of −1.