Regular Tetrahedron Calculator
Compute the volume, surface area, height and sphere radii of a regular tetrahedron from a single edge length.
units
Volume of the regular tetrahedron
- 1
a² (scales surface area)
6² = 36 - 2
Surface area = √3 × a²
√3 × 36 = 62.3538 - 3
Volume = a³ ÷ (6 × √2)
6³ ÷ (6 × √2) = 25.4558Equivalent to (√2/12)·a³ — one third of the prism with equilateral-triangle base.
How does this calculator work?
For a regular tetrahedron with edge a, the volume is a³/(6√2) and the surface area is √3·a². Its height is a·√(2/3), the inscribed sphere radius is a/(2√6), and the circumscribed sphere radius is a·√6/4 (exactly three times the inradius). Just enter the edge length to get every measurement.
Formula
How this is calculated
A regular tetrahedron is the simplest Platonic solid: four congruent equilateral-triangle faces, four vertices and six edges all of the same length a. Enter the edge length a (in any consistent unit) and every other quantity is derived directly from it.
The volume follows from V = a³/(6√2), the total surface area is the four faces combined, S = √3·a², where each face has area (√3/4)a². The height (from any vertex perpendicular to the opposite face) is h = a·√(2/3). The inscribed sphere, tangent to all four faces, has radius r = a/(2√6), while the circumscribed sphere, passing through all four vertices, has radius R = a·√6/4. Note that R = 3r, a characteristic ratio of the regular tetrahedron.
Results scale predictably: lengths grow linearly with a, areas with a², and volume with a³. The edge must be a positive number; non-positive or non-numeric input is rejected. Outputs use the same length unit as the input (areas squared, volume cubed).
Frequently asked questions
For a regular tetrahedron the circumradius is exactly three times the inradius (R = 3r), since R = a·√6/4 and r = a/(2√6).
A regular tetrahedron has 4 equilateral triangular faces, 6 edges and 4 vertices, all edges being equal in length.
It is unit-agnostic. Whatever unit you use for the edge, the height and radii share it, the surface and face areas are in that unit squared, and the volume in that unit cubed.
Also known as
TG we-Calculate Editorial Team. (2026). Regular Tetrahedron Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/regular-tetrahedron-calculator
TG we-Calculate Editorial Team. "Regular Tetrahedron Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/regular-tetrahedron-calculator.
TG we-Calculate Editorial Team, "Regular Tetrahedron Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/regular-tetrahedron-calculator
@misc{wecalculate_regular_tetrahedron_calculator, title = {Regular Tetrahedron Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/regular-tetrahedron-calculator}}, year = {2026}, note = {TG we-Calculate} }
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