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Tetrahedron Volume Calculator

Work out tetrahedron volume instantly with clear inputs, formula shown and shareable results.

About Tetrahedron Volume Calculator

A regular tetrahedron has four equilateral triangular faces. Its volume is a³/(6√2) and its surface area √3·a², being four triangles of area (√3/4)a² each.

Formulas

Volume

V = a³ / (6√2) = (√2/12)a³

Surface area

S = √3·a²

Height

h = a√(2/3)

Worked example

With the default values below, Tetrahedron Volume Calculator returns Volume of 25.4558. Change any input above and every figure here is recalculated in your browser.

Inputs used

Edge lengthminimum 0
6
Number of solidsminimum 1
1

Results

Volume
25.4558
Surface area (4 triangles)
62.3538
Height from a face to the apex
4.8990
Combined volume
25.4558

Step by step

  1. 1Values used
  2. 2Volume
  3. 3Surface area
  4. 4Height
  5. 5Volume= 25.4558
  6. 6Surface area (4 triangles)= 62.3538
  7. 7Height from a face to the apex= 4.8990
  8. 8Combined volume= 25.4558

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many faces, edges and vertices?

Four faces, six edges and four vertices, satisfying Euler's 4 − 6 + 4 = 2.

Edge 6 gives what volume?

216 / (6√2) = 36/√2 ≈ 25.455844 cubic units.

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