Math
Regular tetrahedron
Find the volume, surface area and height of a tetrahedron with six equal edges.
Calculators / Math / Regular octahedron
Regular octahedron calculator
Calculate the volume and surface area of a solid with eight equal equilateral faces.
On this page
Volume12.73units³
Surface area31.18units²
Opposite-vertex distance4.24units
Calculator controls
How to calculate
Calculate the volume and surface area of a solid with eight equal equilateral faces.
Volume =
sqrt(2)*a^3/3 units³Surface area =
2*sqrt(3)*a^2 units²Opposite-vertex distance =
sqrt(2)*a unitsWorked example
- Edge length: 3
- Volume: 12.73 units³
- Surface area: 31.18 units²
- Opposite-vertex distance: 4.24 units
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate the volume and surface area of a solid with eight equal equilateral faces. An octahedron can be viewed as two equal square pyramids joined at their bases.
When this tool is useful
An octahedron can be viewed as two equal square pyramids joined at their bases.
Understanding your inputs
| Input | Example |
|---|---|
Edge length a | 3 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.