Tetrahedron Volume Calculator

Created by Luciano Mino
Last updated: Jul 11, 2022

The tetrahedron volume calculator makes finding the volume of a tetrahedron as simple as typing a single parameter!

This tool can output a lot of information about any regular tetrahedron 🔺, including:

  • Volume of a tetrahedron;
  • Surface area of a tetrahedron;
  • Height of a tetrahedron;
  • Insphere, midsphere, and circumsphere radius of a tetrahedron; and
  • Surface to volume ratio of a tetrahedron.

Keep reading to know what a tetrahedron is and learn more about the volume of a tetrahedron formula.

What is a tetrahedron?

From its name, "tetra" means four, and "hedron" refers to a solid geometrical figure containing a specific number of faces.

Therefore, a tetrahedron is a three-dimensional figure with four faces or sides.

This definition gives tetrahedron a pyramid-like form since all its sides will be triangles.

We can distinguish between two general types of tetrahedrons:

  • Regular tetrahedrons, where their faces are equilateral triangles; and
  • Irregular tetrahedrons, where their faces are not equilateral triangles.

We will work with regular tetrahedronsin this tetrahedron volume calculator.

🔎 If you want to find the volume of other three-dimensional figures, check the cylinder volume calculator and the sphere volume calculator!

Volume, surface area, and height of a tetrahedron formulas

We can find the volume, surface area, and height of a tetrahedron with just a single parameter: edge length (LL), the length of any of its sides.

Volume of a tetrahedron formula

The volume VV of a tetrahedron can be written as:

V=L36×2V = \frac{L^{3}}{6\times \sqrt{2}}

Surface area of a tetrahedron

Similarly, the total surface area AA of a tetrahedron is:

A=3×L2A = \sqrt{3}\times L^{2}

We can also find the surface-to-volume ratio SVR\text{SVR} by dividing these previous equations:

SVR=AV=3×L2L36×2SVR=66L\text{SVR} =\frac{A}{V} = \frac{\sqrt{3}\times L^{2}}{\frac{L^{3}}{6\times \sqrt{2}}} \\ \text{SVR}= \frac{6\sqrt{6}}{{L}}

Height of a tetrahedron

And lastly, we can calculate the height HH of a tetrahedron with the following formula:

H=63×LH = \frac{\sqrt{6}}{3} \times L

🙋 Using the tetrahedron volume calculator, you don't have to remember any formula. Just input the edge length, and the calculator will automatically output all of these parameters for you!

Tetrahedron spheres

The tetrahedron volume calculator can also find the radius of the insphere, midsphere, and circumsphere.

What are these spheres? Let's look at their definitions:

  • Insphere – this sphere is tangent to every face of the tetrahedron. We can calculate its radius rir_{i} with: ri=L24r_{i} = \frac{L}{\sqrt{24}}.
  • Midspheretangent to every edge of the tetrahedron. Its radius is: rk=L8r_{k} = \frac{L}{\sqrt{8}}.
  • Circumspehreall the vertices of the tetrahedron lie on this surface. Lastly, we can find the circumsphere's radius with: ru=L×64r_{u} = \frac{L \times \sqrt{6}}{4}
Luciano Mino
Edge length (L)
ft
Height of tetrahedron (H)
ft
Volume of tetrahedron (V)
cu in
Surface Area
Surface area of tetrahedron (A)
in²
Surface to volume ratio (SVR)
1/
in
Spheres of Tetrahedron
Insphere radius (Rᵢ)
ft
Midsphere radius (Rₖ)
ft
Circumsphere radius (Rᵤ)
ft
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