Math
Tetrahedron Calculator
A regular tetrahedron is the triangular pyramid with four identical equilateral faces.
Everything about it is a fixed multiple of the edge, so the tetrahedron calculator solves the whole solid from one measurement — edge, volume, surface area, or height — and keeps the answers exact (edge 6 gives surface area 36√3 and height 2√6).
Surface area in square units, volume in cubic units, edge and height are lengths.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Volume
—
- Volume (exact)
- —
- Edge
- —
- Surface area (4 faces)
- —
- One face
- —
- Height
- —
- Inradius / midradius / circumradius
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the tetrahedron calculator solves
A regular tetrahedron is the triangular pyramid with four identical equilateral faces. Everything about it is a fixed multiple of the edge, so the tetrahedron calculator solves the whole solid from one measurement — edge, volume, surface area, or height — and keeps the answers exact (edge 6 gives surface area 36√3 and height 2√6).
Formula
How to use it
- Choose the measurement you know: edge, volume, surface area, or height.
- Enter it and pick a unit.
- Read the edge, volume, surface area, face area, height, and the three sphere radii; the exact A root expression written with the √ symbol, such as a square root. appears whenever the value is a clean multiple of √2, √3, or √6.
How to read the answer
The height runs from one The turning point of a parabola, or a corner point of a shape. straight down to the center of the opposite face and is about 0.8165 times the edge. The inradius is the sphere that touches all four faces, the circumradius the sphere through all four vertices (exactly three times the inradius), and the midradius the sphere tangent to all six edges.
Common mistakes and edge cases
- Using the triangular pyramid formula with a face height instead of the true vertical height — the height is a√(2/3), not the face's altitude a√3/2.
- Assuming the volume is one third of a cube — a tetrahedron with edge a fills only about 11.8% of the cube with the same edge.
- This page is for regular tetrahedra only; an irregular one needs all six edge lengths or coordinates.
- Zero or negative measurements are rejected.
Worked examples
Edge 6 (surface 36√3, height 2√6)
Volume
25.4558
Volume 100 → edge
Volume
100
Surface area 100
Volume
51.7003
Height 5
Volume
27.0633
Decimal edge 2.5
Volume
1.8414
Unit edge (a = 1)
Volume
0.1179
Zero edge (impossible)
Volume
Error
Frequently asked questions
What is the volume of a regular tetrahedron?+
V = a³/(6√2) ≈ 0.11785·a³. Edge 6 gives 216/(6√2) = 36/√2 = 18√2 ≈ 25.46.
What is the surface area of a tetrahedron?+
Four equilateral triangles: SA = 4 × (√3/4)a² = √3·a². Edge 6 gives 36√3 ≈ 62.35.
How tall is a regular tetrahedron?+
h = a·sqrt(2/3) ≈ 0.8165a, measured from a vertex to the center of the opposite face. Edge 6 gives 2√6 ≈ 4.899.
How do I find the edge from the volume?+
a = cbrt(6√2·V). A volume of 100 gives an edge of about 9.467.
What are the inradius and circumradius of a tetrahedron?+
Inradius r = a/(2√6) = a√6/12 (sphere touching the faces); circumradius R = a√6/4 (sphere through the vertices). R is exactly 3r.
Is a tetrahedron the same as a triangular pyramid?+
Every tetrahedron is a triangular pyramid. 'Regular' means all four faces are identical equilateral triangles, which is what this calculator assumes.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Cube Calculator
Enter one cube measurement — edge, face diagonal, space diagonal, surface area, or volume — and get all five, with exact radicals (s√2, s√3), face area, inscribed and circumscribed sphere radii, and liters.
Volume Calculator
Find the volume of 11 solids — cube, box, cylinder, cone, sphere, hemisphere, pyramid, triangular prism, ellipsoid, capsule, and frustum — with exact π forms, cubic-unit labels, surface area, and liters/gallons capacity.
Pyramid Volume Calculator
Calculate rectangular pyramid volume from base length, base width, and perpendicular height.
Surface Area Calculator
Find the total surface area of a cube, box, cylinder, cone, sphere, rectangular pyramid, or triangular prism with the formula for each solid, the lateral and base breakdown, exact π forms, and square-unit labels.
Triangle Area Calculator
Calculate triangle area from base and height with unit-friendly steps.
Area Calculator
Find the area of 11 shapes — rectangle, square, triangle (base-height, three sides, or SAS), circle, trapezoid, parallelogram, rhombus, ellipse, regular polygon, sector, and kite — with the formula, substitution, square-unit labels, and a diagram.
Last updated: September 4, 2026