Tetrahedron Calculator

Understanding the Regular Tetrahedron

A regular tetrahedron is the simplest Platonic solid — a three-dimensional shape with four congruent equilateral-triangle faces, four vertices, and six edges of equal length. It is the only Platonic solid that is self-dual, meaning its dual is another regular tetrahedron. The tetrahedron appears throughout mathematics, chemistry, and engineering: from the geometry of methane molecules (CH₄) to lightweight space-frame trusses. For other Platonic solids, try our Octahedron Calculator and Dodecahedron Calculator.

Regular Tetrahedron Formulas

All geometric properties of a regular tetrahedron can be derived from a single parameter: the edge length $a$. The following formulas describe its key measurements:

• Volume ($V$): The space enclosed by the four triangular faces: $$V = \frac{a^3}{6\sqrt{2}} \approx 0.117851 a^3$$
• Surface Area ($S$): The combined area of all four equilateral-triangle faces: $$S = \sqrt{3} a^2 \approx 1.732051 a^2$$
• Height ($h$): The perpendicular distance from any vertex to the opposite face: $$h = a \sqrt{\frac{2}{3}} = \frac{a \sqrt{6}}{3} \approx 0.816497 a$$
• Circumradius ($R_u$): The radius of the sphere passing through all four vertices: $$R_u = \frac{a \sqrt{6}}{4} \approx 0.612372 a$$
• Inradius ($R_i$): The radius of the sphere tangent to all four faces: $$R_i = \frac{a}{2\sqrt{6}} \approx 0.204124 a$$
• Dihedral Angle ($\theta$): The angle between any two adjacent faces: $$\theta = \arccos\left(\frac{1}{3}\right) \approx 70.5288^\circ$$

How to Use the Tetrahedron Calculator

This calculator allows you to input any known dimension of a regular tetrahedron and instantly computes all other parameters.

1. Select the known parameter from the dropdown menu (Edge Length, Volume, Surface Area, or Height).
2. Enter the value of the chosen parameter in the input field.
3. The tool automatically calculates and displays all other properties in real time — edge length, volume, surface area, height, inradius, circumradius, and dihedral angle.
4. Use the Details text area to view the exact values and copy the output for your records.