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Regular Tetrahedron Surface Area

Also known as surface area of a tetrahedron

A=3 s2A = \sqrt{3}\,s^2

Worked example: edge 2 m → 4 sqrt(3) m^2 (6.9282032 m2) — press Try an example to run it live, then adjust anything.

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Constant used — built into this formula, no need to enter
3=1.7320508075688772\sqrt{3} = 1.7320508075688772Square Root of Three · exact
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Regular Tetrahedron Surface Area explained

sA

Four equilateral triangles, each with area 34s2\tfrac{\sqrt{3}}{4}s^2, sum to the memorable A=3 s2≈1.732s2A = \sqrt{3}\,s^2 \approx 1.732s^2. It is one of the tidiest results in solid geometry: the surface of a tetrahedron of edge ss is smaller than the surface of a single square of side 1.32s1.32s.

Compare it with the cube of the same edge, which carries 6s26s^2 of surface, and the tetrahedron looks almost frugal. But compare surface to volume instead and the picture inverts. The tetrahedron is the worst of the Platonic solids at enclosing volume per unit of skin, which is one reason bubbles and droplets are never tetrahedral, and why the shape survives in engineering only where stiffness, not efficiency, is the goal.

Regular Tetrahedron Surface Area formula

A=3 s2A = \sqrt{3}\,s^2
Where
  • AA= Surface area (m²)
  • ss= Edge length (m)

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