Quick answer: the volume of a cube is V = a³ — the edge length multiplied by itself twice. A 4 cm cube holds 64 cm³; a 10 cm cube holds exactly 1 liter. Started from a diagonal? Edge = diagonal ÷ √3 (space diagonal) or ÷ √2 (face diagonal).
The cube volume formula — and its relatives
from space diagonal d: a = d/√3 · from face diagonal f: a = f/√2 · from surface area S: a = √(S/6)
Worked example — a shipping crate with 30-inch edges:
- Cube the edge: 30 × 30 × 30 = 27,000 in³
- Convert: 27,000 ÷ 1,728 = 15.6 ft³ — the number a mover or freight quote runs on.
The cube is the simplest 3-D shape, but it punches above its weight as a mental unit: metric volume is built on it. One cubic centimeter is a 1-cm cube; a liter is a 10-cm cube; a cubic meter is 1,000 of those liters stacked 10 × 10 × 10.
Note the third conversion above runs the other way: if you know the area to be painted or wrapped rather than the edge, S = 6a² inverts to a = √(S/6). The surface area calculator handles that side of the pair, and because a cube's volume grows as a³ while its skin grows only as a², the two diverge fast — the effect quantified by the surface-area-to-volume ratio.
Edge → volume — quick reference
| Edge | Volume (a³) | If cm → liters | If ft → US gal |
|---|---|---|---|
| 1 | 1 | 0.001 | 7.48 |
| 2 | 8 | 0.008 | 59.8 |
| 3 | 27 | 0.027 | 202 |
| 4 | 64 | 0.064 | 479 |
| 5 | 125 | 0.125 | 935 |
| 6 | 216 | 0.216 | 1,616 |
| 8 | 512 | 0.512 | 3,830 |
| 10 | 1,000 | 1.0 | 7,481 |
| 12 | 1,728 | 1.728 | 12,927 |
Note the row at 12: a 12-inch cube is 1,728 in³ — exactly one cubic foot. That's where the odd-looking 1,728 conversion factor comes from.
Where cube volume shows up in real life
Concrete test cubes
Outside North America, concrete strength is tested by crushing 150-mm cubes. Each holds 15³ = 3,375 cm³ ≈ 3.4 liters and weighs about 8 kg — worth knowing before you carry six of them across a site.
Storage and shipping
"Cube" is literally freight slang for volume. A 24-inch storage cube holds 13,824 in³ = 8 ft³; a mover's book rates a stack of six at 48 ft³. When a quote says you've "cubed out," your load hit the volume limit before the weight limit — the freight volume calculator covers the CBM math carriers use.
Aquariums and terrariums
Cube tanks are popular because they maximize volume for their footprint. A 40-cm cube nano tank: 64,000 cm³ = 64 liters ≈ 16.9 US gallons — before subtracting substrate and rock. The aquarium calculator handles those deductions.
Common mistakes & pro tips
- Multiplying by 3 instead of cubing. a³ means a × a × a. A 5-cm cube is 125 cm³, not 15.
- Assuming it's actually a cube. Measure a second edge. If length, width and height differ at all, use the box calculator — a "roughly cubic" 30 × 30 × 28 box loses 6% of the volume you'd otherwise book.
- Diagonal entered as edge. The space diagonal is 73% longer than the edge, which would inflate the volume 5.2×. Divide by √3 first.
- Pro tip — the liter anchor. Memorize "10-cm cube = 1 L". It converts metric volumes in your head: a 30-cm cube is 3× bigger per side, so 27 liters, instantly.
How to use this calculator
- Measure one edge. All twelve edges of a cube are identical, so one measurement is enough. Verify with a second edge if precision matters — many "cubes" are actually slightly rectangular.
- Cube it. Multiply the edge by itself twice: V = a × a × a. A 4 cm edge gives 64 cm³.
- Convert if needed. Switch the output between cubic units, liters and gallons — a 10 cm cube is exactly 1 liter.
Frequently asked questions
What is the formula for the volume of a cube?
V = a³, where a is the edge length. It's the box formula l × w × h with all three dimensions equal. A cube with 5-inch edges holds 5³ = 125 in³.
How do I find cube volume from the diagonal?
The space diagonal of a cube is d = a√3, so the edge is a = d ÷ 1.732. A cube whose corner-to-opposite-corner diagonal measures 10 cm has edges of 5.77 cm and a volume of 192.5 cm³. For the face diagonal (across one square face), divide by √2 = 1.414 instead.
How do I find cube volume from the surface area?
A cube has six identical square faces, so the edge is a = √(S ÷ 6). A cube with 150 cm² of total surface has edges of √25 = 5 cm and a volume of 125 cm³.
How many liters are in a 10 cm cube?
Exactly one. 10 × 10 × 10 = 1,000 cm³ = 1 liter — this is literally how the liter was defined. It's the fastest sanity check in metric volume work: picture how many 10-cm cubes fit in your container.
What happens to the volume if I double the edge?
It multiplies by 8 (2³). Triple the edge and it multiplies by 27. This cube-scaling is why a moving box that looks 'a bit bigger' holds dramatically more — and weighs dramatically more when full.