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.

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.

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:

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: $r_{u} = \frac{L \times \sqrt{6}}{4}$