# 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.

## 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 ($L$), the length of any of its sides.

### Volume of a tetrahedron formula

The volume $V$ of a tetrahedron can be written as:

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

### Surface area of a tetrahedron

Similarly, the total surface area $A$ of a tetrahedron is:

$A = \sqrt{3}\times L^{2}$

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

$\text{SVR} =\frac{A}{V} = \frac{\sqrt{3}\times L^{2}}{\frac{L^{3}}{6\times \sqrt{2}}} \\ \text{SVR}= \frac{6\sqrt{6}}{{L}}$

### Height of a tetrahedron

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

$H = \frac{\sqrt{6}}{3} \times L$

🙋 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 $r_{i}$ with: $r_{i} = \frac{L}{\sqrt{24}}$.
• Midspheretangent to every edge of the tetrahedron. Its radius is: $r_{k} = \frac{L}{\sqrt{8}}$.
• Circumspehreall the vertices of the tetrahedron lie on this surface. Lastly, we can find the circumsphere's radius with: $r_{u} = \frac{L \times \sqrt{6}}{4}$
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
ft
ft
ft
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