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Tetrahedron Calculator

Find a tetrahedron’s volume and surface area.

Result

14.73
43.30

How it is calculated

A regular tetrahedron has four identical equilateral triangle faces, so one edge length a fixes everything. The volume is V = a3 / (6√2) and the total surface area is A = √3 × a2, which is four triangles of area (√3/4) a2 each. The edge must be above zero and the same unit is used throughout: if the edge is in cm, the volume is in cm³ and the area in cm². Both results are rounded to two decimals. A tetrahedron whose faces are not all equal needs different formulas.

Worked example

Edge length a = 5. Volume = 53 / (6√2) = 125 / 8.485 = 14.73 cubic units. Surface area = √3 × 52 = 1.732 × 25 = 43.30 square units. Doubling the edge would multiply the volume by 8 but the area by only 4.

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Common mistakes

  • Entering a height or face diagonal instead of the edge length.
  • Reporting the volume in square units, or the area in cubic units; volume scales with the cube of the edge, area with the square.
  • Using the formulas for a square-based pyramid or an irregular tetrahedron, whose faces are not all equilateral triangles.
  • Mixing units, such as an edge in millimetres and a volume expected in cubic centimetres.

About this calculator

This calculator finds the volume and surface area of a regular tetrahedron — a three-dimensional shape made of four identical equilateral triangle faces — from a single edge length, using formulas derived from the shape's symmetry, where the surface area is simply four times the area of one equilateral triangular face and the volume follows from the geometry of the shape's apex height above its triangular base.

This is a standard topic in solid geometry and chemistry-adjacent coursework, since the tetrahedron is the simplest of the Platonic solids and appears in crystallography and molecular geometry, such as the tetrahedral arrangement of atoms bonded to a central carbon atom. It's also used in engineering, 3D modeling and architecture whenever tetrahedral trusses, frames or structural units are being sized, since a single edge measurement is enough to determine both how much material covers the shape's surface and how much volume it encloses.

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