A regular tetrahedron is the most symmetric of the Platonic solids — 4 identical equilateral triangular faces, 4 vertices, and 6 equal edges. Because every edge is the same length, one number (the edge length a) is enough to derive the volume, surface area, height, and per-face area. This calculator does that instantly and explains how each value follows from the others.
How the Tetrahedron Calculator works
The calculator starts from the edge length a and applies three closed-form formulas derived from the tetrahedron's geometry. Volume is V = a³ / (6√2) — the tetrahedron occupies exactly 1/(3√2) of the volume of a cube with the same edge length. Surface area is SA = √3 × a², the sum of the 4 equilateral triangular faces, each with area (√3/4) × a². Height — the perpendicular distance from a face to the opposite vertex — is h = a × √(2/3), which comes from the 3D Pythagorean relationship between the edge and the centroid of the base triangle.
Inputs and what they mean
The only input is the edge length, entered in inches, feet, centimeters, or meters. Because a regular tetrahedron has all 6 edges equal, this single measurement fully determines the shape — there's no separate base or width to enter, unlike a rectangular pyramid. The unit selector is a display label only: volume results show cubed units and surface area results show squared units automatically, but the calculator does not convert between unit systems, so keep your edge-length entry in the unit you selected.
Limits and edge cases
This calculator assumes a regular tetrahedron — all faces are congruent equilateral triangles. An irregular tetrahedron (four triangular faces of different sizes, as in some crystal structures or 3D-modeling contexts) needs a full 3D coordinate-based calculation instead, since volume and surface area no longer reduce to a single edge-length formula. For a pyramid with a square or rectangular base rather than a triangular one, use the dedicated Pyramid Calculator; for a general triangular pyramid with three different edge lengths, a vector-based volume formula (one-sixth the absolute value of the scalar triple product of three edge vectors) is required instead of the formulas here.