# Tetrahedron Volume Calculator

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 tetrahedrons**in 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:

### Surface area of a tetrahedron

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

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

### Height of a tetrahedron

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

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