Tetrahedron Calculator
Volume, surface area and height of a regular tetrahedron.
Volume
14.7314
regular tetrahedron (4 faces)
Surface area
43.3013
Faces / edges / vertices
4 / 6 / 4
Height
4.0825
AI Breakdown & Smart Takeaway
Plain-English insight on your numbers
Get a personalized explanation of what these results mean — and how to improve them.
How the Tetrahedron Calculator works
The GKCalculators Tetrahedron Calculator instantly computes the volume, total surface area, and height of any regular tetrahedron from a single edge-length input — perfect for students, engineers, architects, game developers, and anyone working with 3D geometry.
A regular tetrahedron is one of the five classical Platonic solids: a three-dimensional shape composed of exactly four equilateral triangular faces, four vertices, and six equal edges. Because every face and every edge is identical, the entire geometry of the solid is determined by just one measurement — the edge length (a). This elegant property is what makes the calculator so simple to use: you enter a single value and receive all three key measurements instantly.
The volume of a regular tetrahedron scales with the cube of the edge length, while the surface area scales with the square of the edge length, and the height scales linearly. This means small changes in edge length produce disproportionately large changes in volume — doubling the edge length increases volume by a factor of eight. Understanding this non-linear relationship is critical when scaling tetrahedra for real-world applications like packaging design, molecular modeling, or architectural frameworks.
Height in a regular tetrahedron refers specifically to the perpendicular distance from any vertex down to the centroid of the opposite face. It is not the same as the edge length or the slant height of a face. Many users confuse the face height (the altitude of one equilateral triangle) with the solid's overall height, which leads to significant calculation errors — the solid's true height is always shorter than the face altitude by a factor of √(2/3).
When entering measurements, make sure your units are consistent. If you input the edge length in centimeters, the calculator returns surface area in square centimeters and volume in cubic centimeters. Mixing units — for example, entering the edge in inches but expecting volume in liters — is the most common source of incorrect results. Always convert to a single unit system before calculating, and remember that 3D geometry amplifies unit mismatches dramatically due to the cubic relationship in volume.
Formula
V = a³ / (6√2), SA = √3 · a²
Pro tips
- Always use consistent units before entering your edge length — convert everything to the same unit first, because volume errors compound cubically and a small unit mismatch becomes a massive numerical error.
- If you know the height of your tetrahedron rather than the edge length, rearrange the height formula: a = h / √(2/3). Solve for 'a' first, then enter it into the calculator.
- For 3D printing or physical modeling, add a small tolerance margin (typically 1–2%) to your surface area result to account for material waste, seams, or coating thickness.
- Remember that the face height (altitude of one triangular face) equals (√3/2)·a, which is always larger than the solid's overall height. Don't substitute one for the other in structural or spatial calculations.
- When comparing a tetrahedron to a cube or sphere of the same edge length, note that the tetrahedron encloses the least volume relative to its surface area — it is the least efficient Platonic solid volumetrically, which matters in packaging and materials science.
Key terms
- Regular Tetrahedron
- — A Platonic solid with four congruent equilateral triangular faces, four vertices, and six equal-length edges.
- Edge Length (a)
- — The length of any one edge of the regular tetrahedron, which fully determines all other geometric properties of the solid.
- Volume
- — The three-dimensional space enclosed by the tetrahedron, calculated as a³ divided by 6√2.
- Surface Area
- — The combined area of all four equilateral triangular faces, equal to √3 multiplied by the square of the edge length.
- Height (Altitude)
- — The perpendicular distance from one vertex to the centroid of the opposite face, equal to the edge length multiplied by √(2/3).
- Platonic Solid
- — A convex 3D polyhedron whose faces are congruent regular polygons with the same number meeting at each vertex; the tetrahedron is the simplest of the five Platonic solids.
