Volume of a regular tetrahedron calculator
Enter the dimensions of a regular tetrahedron and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
7.542 472 3m³
- Surface area
- 27.712 813
- Height
- 3.265 986 3
- Insphere radius
- 0.816 496 58
Show the working
- Edge length = 4
- Volume = 4^3 / (6 * sqrt(2)) = 7.542 47
- Surface area = sqrt(3) * 4^2 = 27.7128
- Height = 4 * sqrt(2/3) = 3.265 99
- Insphere radius = 4 / (2*sqrt(6)) = 0.816 497
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- volume = e^3 / (6 sqrt 2)
- surface area = sqrt 3 x e^2
Switch the volume unit to litres or US gallons to read the capacity directly.