Calculators
Regular Tetrahedron Calculator
Calculate regular tetrahedron volume, surface area, height, insphere radius, and circumsphere radius from its edge length.
Measure a regular tetrahedron from one edge.
A regular tetrahedron has four equilateral triangle faces and six equal edges. For edge length a, volume = a³/(6√2), total surface area = √3a², single face area = √3a²/4, height = √(2/3)a, insphere radius = a/√24, and circumsphere radius = √(3/8)a. The insphere touches all four faces; the circumsphere passes through all four vertices. For a = 6, volume ≈ 25.4558441227 cubic units, surface area ≈ 62.3538290725 square units, and height ≈ 4.89897948557 units. These formulas apply only to regular tetrahedra. Enter a positive edge length from 1e-50 to 1e50 using one consistent unit; areas use square units and volume uses cubic units. Results use browser floating-point arithmetic rounded to 12 significant digits. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the volume of a regular tetrahedron?
Volume = a³/(6√2), where a is the shared edge length. For edge length 6, the volume is approximately 25.4558441227 cubic units.
How is surface area calculated?
Each equilateral triangle face has area √3a²/4. Multiply by four for total surface area √3a².
What do the two sphere radii mean?
The insphere is tangent to all four faces and has radius a/√24. The circumsphere passes through all vertices and has radius √(3/8)a, three times the insphere radius.
Can I use this for an irregular tetrahedron?
No. These formulas require all six edges to be equal. Height is the perpendicular distance from a vertex to its opposite face.
Which units and inputs are accepted?
Enter an edge length from 1e-50 to 1e50, including decimals or scientific notation. Use any length unit consistently. Calculation, copy, and reset run in your browser.