Tetrahedron Volume Calculator
Find the volume of a regular tetrahedron.
Results update as you type.
How it works
A regular tetrahedron is a pyramid with four identical equilateral-triangle faces, the simplest of the Platonic solids, and this calculator finds its key measurements from a single edge length. You enter the edge length, and it returns the volume, the total surface area, and the height. Because all edges of a regular tetrahedron are equal and all faces are congruent equilateral triangles, every measurement follows from that one length. The volume is the edge cubed divided by six times the square root of two, a compact formula reflecting the solid's high symmetry. The surface area is simply four times the area of an equilateral triangle, which works out to the square root of three times the edge squared. The height, the perpendicular distance from any vertex to the opposite face, is the edge times the square root of two-thirds. Tetrahedra appear in chemistry, where molecules like methane have a tetrahedral shape, in engineering trusses and space frames for their rigidity, in crystallography, and in games and design. Their strength and symmetry make them structurally important. This calculator handles the regular tetrahedron, where all edges are equal; irregular tetrahedra with different edge lengths need more information to compute. The edge length must be positive. Enter the edge length to find the tetrahedron's volume, surface area, and height.
V = a³ / (6√2) ; Surface area = √3 · a²
A regular tetrahedron has four identical equilateral-triangle faces. From its edge length a, the volume is a cubed divided by six times the square root of two, the surface area is the square root of three times a squared (four equilateral triangles), and the height from a vertex to the opposite face is a times the square root of two-thirds.
Source:Solid geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter edge length (a).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Volume updates instantly as you type — no button to press.
Frequently asked questions
What is a regular tetrahedron?
A regular tetrahedron is a three-dimensional shape with four faces, all identical equilateral triangles, and four vertices where three faces meet. It is the simplest of the five Platonic solids and can be thought of as a triangular pyramid with all edges equal. Its complete symmetry means every measurement depends only on the edge length.
How do you find a tetrahedron's volume?
For a regular tetrahedron, the volume is the edge length cubed divided by six times the square root of two. This single formula gives the volume directly from the edge. The calculator computes it along with the surface area and height, so you get all the main measurements from one input.
How is the surface area calculated?
A regular tetrahedron has four equilateral-triangle faces, so its surface area is four times the area of one equilateral triangle. This simplifies to the square root of three times the edge length squared. The calculator reports this total surface area, useful for coating, wrapping, or material calculations on tetrahedral objects.
What is the height of a tetrahedron?
The height is the perpendicular distance from one vertex to the center of the opposite triangular face. For a regular tetrahedron it equals the edge length times the square root of two-thirds. This height is useful for fitting a tetrahedron into a space or understanding its proportions relative to its base.
Where do tetrahedra appear in the real world?
Tetrahedral shapes occur in chemistry, where molecules such as methane arrange their atoms tetrahedrally, in crystal structures, and in engineering trusses and space frames that exploit the tetrahedron's rigidity. They also appear in dice, packaging, and art. Their combination of strength and symmetry makes them both structurally and aesthetically significant.