From edge length
For a = 6 cm, h = 6√(2/3) ≈ 4.8990 cm, S = 36√3 ≈ 62.3538 cm², and V = 216/(6√2) ≈ 25.4558 cm³.
Tetrahedron Calculator — Volume, Surface Area and Height
Diagram & Known Measurement
Enter one value. You may enter more to check whether rounded measurements describe the same regular tetrahedron.
Results
Enter one positive measurement to begin.
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How to Use the Tetrahedron Calculator
- Enter one positive value: edge length, perpendicular height, total surface area, area of one face, or volume.
- Choose the unit beside that value and select the length unit you want for the results.
- Select Calculate. The tool derives the edge first, then calculates every other measurement and shows the working.
Important assumption: this tool calculates a regular tetrahedron, so all four faces are congruent equilateral triangles and all six edges have equal length. An irregular tetrahedron needs additional measurements.
Regular Tetrahedron Formulas
Let a be the common edge length. These formulas use ordinary Euclidean geometry.
| Measurement | Formula from edge a | Edge from measurement |
|---|---|---|
Height h | h = a√(2/3) | a = h√(3/2) |
One-face area A | A = √3a²/4 | a = √(4A/√3) |
Total surface area S | S = √3a² | a = √(S/√3) |
Volume V | V = a³/(6√2) | a = ∛(6√2V) |
Inradius r | r = a√6/12 | — |
Circumradius R | R = a√6/4 | — |
The surface area is exactly four times one-face area. The center divides the height in a 3:1 ratio, so R = 3r and h = R + r.
Accuracy and Units
Formula check: results use S = √3a², V = a³/(6√2) and h = a√(2/3), plus their algebraic rearrangements.
Length units become squared for area and cubed for volume. Conversions occur before calculations, and rounding is applied only to displayed results. Very small and very large results use scientific notation.
Calculations run locally in your browser. Last reviewed: July 30, 2026.
Worked Examples
From surface area
For S = 100 cm², a = √(100/√3) ≈ 7.5984 cm. The height is approximately 6.2040 cm.
From volume
For V = 1000 mm³, a = ∛(6000√2) ≈ 20.3965 mm. The total surface area is approximately 720.5622 mm².
Tetrahedron Calculator FAQs
What kind of tetrahedron does this calculator solve?
It solves a regular tetrahedron: a solid made from four congruent equilateral-triangle faces, with all six edges equal.
How do you calculate the volume of a regular tetrahedron?
For edge length a, volume is V = a³/(6√2), equivalent to √2a³/12.
How do you find the surface area of a regular tetrahedron?
The total surface area is S = √3a². Each of the four equilateral faces has area √3a²/4.
How do you find the height of a regular tetrahedron?
The perpendicular height from a vertex to the opposite face is h = a√(2/3).
Can I find edge length from volume?
Yes. Rearranging the volume formula gives a = ∛(6√2V).
What is the difference between the inradius and circumradius?
The inradius runs from the center to a face and equals a√6/12. The circumradius runs from the center to a vertex and equals a√6/4, three times the inradius.
Can I mix units between inputs?
Yes. Each input has its own unit. If you enter more than one value, the calculator converts them to a common scale and checks whether they describe the same tetrahedron.
Are my measurements uploaded?
No. The calculation runs locally in your browser, and the tool does not send or store your measurements.