A cube has six equal square faces. Dice, sugar cubes, storage boxes and Rubik’s cubes are cubes, and “cubing” a number comes from its volume. It is also the easiest solid for packing and stacking.
How to use the Cube Calculator
- Edge a
- Every result field is editable: type into Volume or any other result and Edge a plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Enter the edge length, or type into the volume, area or a diagonal field and the edge is worked out backwards.
What each result means
- Volume = [Edge a]^3
- Surface area = 6×[Edge a]^2
- Face diagonal = [Edge a]×sqrt(2)
- Space diagonal = [Edge a]×sqrt(3)
- Inscribed sphere radius = [Edge a]÷2
- Circumscribed sphere radius = [Edge a]×sqrt(3)÷2
- Surface to volume ratio = 6÷[Edge a]
Example values
How the main result changes when Edge a changes and everything else stays at the example values above:
| Edge a (cm) | Volume (cm³) |
|---|---|
| 2.5 | 15.625 |
| 3.75 | 52.7344 |
| 5 | 125 |
| 6.25 | 244.1406 |
| 7.5 | 421.875 |
| 10 | 1,000 |
Formula
V = a³, A = 6a², face diagonal f = a√2, space diagonal d = a√3
Worked example
Inputs: Edge a: 5 cm.
Results: Volume = 125 cm³; Surface area = 150 cm²; Face diagonal = 7.071068 cm; Space diagonal = 8.660254 cm; Inscribed sphere radius = 2.5 cm; Circumscribed sphere radius = 4.330127 cm; Surface to volume ratio = 1.2 cm⁻¹.
Key terms
- Space diagonal
- A segment joining opposite corners through the inside.
Frequently asked questions
How do I find the edge from the volume?
a = ∛V.
What is the space diagonal of a cube?
a√3, the longest straight line inside it.
How many edges and vertices does a cube have?
12 edges, 8 vertices, 6 faces.
If I double the edge, what happens to the volume?
It becomes 8 times larger.