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Tetrahedron Calculator

Find the volume of a regular tetrahedron.

How it is calculated

The only input is the edge length a, which must be greater than zero. The tool assumes a regular tetrahedron, where all six edges are equal. Volume is V = a³ ÷ (6 × √2) and total surface area is A = √3 × a². The volume is shown to four decimals and the area to two. Results are labelled units³ and units², meaning they use whatever length unit you typed: enter centimeters and the volume is in cubic centimeters. Zero or negative edges give no result. An irregular tetrahedron, with unequal edges, cannot be computed here because the formulas depend on all edges being the same.

Worked example

A regular tetrahedron has an edge of 6. Cube the edge: 6³ = 216. The divisor is 6 × √2, which is about 8.4853. Volume = 216 ÷ 8.4853, about 25.4558. For the surface, square the edge: 6² = 36, then multiply by √3 (about 1.7321) to get about 62.35. The tool shows 25.4558 units³ for the volume and 62.35 units² for the surface area.

Try this example →

Common mistakes

  • Typing a height or a base-triangle side where the edge is expected. Only the edge length of the solid is used.
  • Applying it to a pyramid with a square base or unequal edges. The formulas hold only for four identical equilateral faces.
  • Mixing units. If the edge is in millimeters, the volume is in cubic millimeters, not liters; convert afterwards, since 1,000 mm³ is not 1 mL.
  • Comparing volumes after doubling the edge and expecting double. Volume scales with the cube, so doubling the edge gives 8 times the volume and 4 times the surface area.
  • Reading the surface result as the area of one face. It is the total of all four faces.

About this calculator

For a regular tetrahedron — four equilateral triangular faces meeting at four vertices — the volume from edge length a is V = a³/(6√2), and the total surface area is the sum of the four equilateral triangle faces, A = √3·a². The volume follows from the tetrahedron's height, h = a·√(2/3), which pins the apex directly above the centroid of the base triangle.

Chemists use this exact geometry to describe molecules with tetrahedral bond arrangements, such as methane (CH₄), where the central atom sits at the tetrahedron's centroid and the four bonds point to its vertices at 109.5°. Crystallographers, architects designing tetrahedral trusses and space frames, and 3D-printing or CAD designers modelling tetrahedral supports all rely on the same volume and surface-area relations.

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