Tetrahedron Volume

This Tetrahedron Volume Calculator computes the volume, surface area, height, face area, and surface-area-to-volume ratio of a regular tetrahedron -- a Platonic solid with 4 equilateral triangle faces. Simply enter the edge length and get instant results with a visual breakdown chart showing all properties of the tetrahedron.

The calculator uses the formula V = a^3/(6sqrt2) for volume, derived from the general pyramid volume formula V = (1/3) x base area x height. Since a regular tetrahedron has all edges equal, its height is H = sqrt(2/3) x a and its base area is (sqrt3/4) x a^2. Substituting these into the pyramid formula gives the simplified tetrahedron volume formula. The surface area is computed as SA = sqrt3 x a^2, which is the area of all 4 equilateral triangle faces combined.

A regular tetrahedron is the simplest of the five Platonic solids. All four faces are congruent equilateral triangles, all six edges have the same length, and all four vertices are equidistant from the center. This makes the tetrahedron a highly symmetric shape with important applications in geometry, chemistry (methane molecule), engineering (space frame structures), and computer graphics (3D mesh generation using tetrahedral elements).

Properties of a regular tetrahedron:

• 4 faces (all equilateral triangles)
• 4 vertices, 6 edges (all equal length)
• Volume: V = a^3/(6sqrt2)
• Surface area: SA = sqrt3 x a^2
• Height: h = a x sqrt(2/3)
• Face area: FA = (sqrt3/4) x a^2
• Surface area to volume ratio: SA:V = 6sqrt6 / a
• Insphere radius: r_i = asqrt6 / 12
• Midsphere radius: r_k = a / sqrt8
• Circumsphere radius: r_u = asqrt6 / 4

The tetrahedron volume calculator is useful for students studying 3D geometry, engineers designing space frame structures, chemists modeling molecular shapes, and anyone working with Platonic solids or polyhedral geometry.