Tetrahedron Volume
Calculator
Results
- Volume
- 14.731391
- Total surface area
- 43.30127
- Height
- 4.082482
Results
| Volume | 14.731391 |
| Total surface area | 43.30127 |
| Height | 4.082482 |
formula-map diagram
- Volume
- 14.731391
- Total surface area
- 43.30127
- Height
- 4.082482
Formula map
Formula
V = a³ ÷ (6√2)= 14.73139127472
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
More in Advanced geometry
See all →Frequently asked questions
What makes a tetrahedron 'regular,' and why does that matter for the formula?+
A regular tetrahedron has four identical equilateral triangle faces and all edges of equal length, which lets the volume be calculated from that single edge length alone. An irregular tetrahedron needs a more complex coordinate-based formula since its faces and edges aren't all the same.
What is the volume formula for a regular tetrahedron?+
Volume is V = (a³)/(6√2), where a is the length of any edge, since all edges are equal in a regular tetrahedron. This simplifies nicely compared to a general tetrahedron, which needs the coordinates of all four vertices.
Why does volume grow with the cube of the edge length rather than a simpler relationship?+
Volume is inherently a three-dimensional quantity, so scaling every linear dimension (edge length) by some factor scales the volume by that factor cubed. Doubling a tetrahedron's edge length increases its volume eightfold (2³ = 8), not just doubling it.
How does a tetrahedron's volume compare to a cube built on the same edge length?+
A regular tetrahedron with edge a has volume about 0.1178a³, while a cube with the same edge a has volume a³, so the tetrahedron holds only about 11.8% as much volume. This makes intuitive sense since the tetrahedron's four triangular faces enclose far less space than a cube's six square faces.
Is a tetrahedron the same as a triangular pyramid?+
Yes, a tetrahedron is simply a triangular pyramid, a pyramid with a triangular base and three triangular sides, making four faces total. It's the simplest possible three-dimensional shape bounded entirely by flat polygonal faces.