Regular Tetrahedron Calculator
From one edge length, get the volume, the total surface area, and the height — the three numbers that describe any regular tetrahedron.
One input, three answers
Enter the edge length and the calculator returns the volume (a³/(6√2)), the surface area (√3·a²), and the height (a·√(2/3)) at once.
Keep units consistent
The edge length is unit-agnostic — your answers come back in the same unit (squared for the surface, cubed for the volume), so don't mix centimetres with inches.
What is a regular tetrahedron calculator?
One edge in, full solid out
A regular tetrahedron is the simplest of the five Platonic solids: a triangular pyramid built from four identical equilateral triangles, with every edge the same length. Because all the edges are equal, a single measurement — the edge length a — fixes the whole shape. This calculator turns that one number into the volume (how much it holds), the total surface area (all four faces), and the height (from a face straight up to the opposite vertex). It is the tool for dice, molecular models, pyramid puzzles, and any geometry homework where a regular tetrahedron shows up.
Enter the edge length in any length unit to get the volume, surface area, and height instantly.
Three short formulas, all built from the single edge length a and a couple of square roots.
volume = a³ / (6√2)The surface area is simply four equilateral-triangle faces, which adds up to √3 × a². The height — the perpendicular distance from any face to the opposite vertex — is a × √(2/3), a little under three-quarters of the edge. The volume, the space inside, is a³ / (6√2): far less than a cube of the same edge, because a tetrahedron tapers sharply to a point.
Suppose you have a regular tetrahedron with an edge length of 6.
Surface area
√3 × 6² = √3 × 36 = 62.353829 square units — all four equilateral faces.
Height
6 × √(2/3) = 4.898979 — from one face to the opposite vertex.
Volume
6³ / (6 × √2) = 25.455844 cubic units — the space inside.
The three outputs answer three different questions. The volume (about 25.455844 cubic units for a = 6) is how much the solid holds — useful for a model, a crystal, or a packing estimate. The single most useful insight is how little a tetrahedron holds for its edge: its volume is roughly one-twelfth (1/(6√2) ≈ 0.1179) of the edge cubed, far less than a cube, because the shape narrows to a single apex. The surface area (about 62.353829 square units) is the total of all four faces — what you would paint or cover, and it scales with the square of the edge, so doubling the edge quadruples the surface. The height (4.898979 here) is the perpendicular drop from a face to the opposite vertex; it is always a fixed fraction √(2/3) ≈ 0.8165 of the edge, which is handy when you need to fit a tetrahedron into a given space. Because every quantity grows from the same single edge, scaling the model up or down is just a matter of rescaling a.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular tetrahedra and consistent units
These formulas describe a perfect regular tetrahedron — four identical equilateral faces with every edge the same length. An irregular tetrahedron (faces of different sizes, edges of different lengths) does not follow these formulas and needs its vertices' coordinates instead. The edge length is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: an edge in centimetres gives a volume in cubic centimetres and a surface area in square centimetres, never a mix.