Find the side length of a cube from its volume, or the volume from a side, in m³, ft³, in³, cm³ or liters, or how many equal cubes fill a volume.
Reverse Volume Formula
The interactive calculator has three cube modes. For total volume V and equivalent cube count N, side s = ∛(V/N), total volume V = N × s³, and count N = V/s³. The box and cylinder formulas below are reference geometry, not additional interactive modes.
- V = known total volume; N = equivalent cube count (1 for a single cube)
- s = cube side length
- a, b = known box sides; c = missing box side
- r = cylinder radius; d = diameter; h = height
The calculator converts volume and side length to cubic meters and meters before applying the cube formulas. Volume, side length and equivalent count must be positive. Fractions of a cube count represent volumes; actual whole-cube capacity also depends on container shape and clearances. Geometry lengths use the unit you entered, unless you choose another output unit.
Reference Tables
Use these to sanity-check a result or to convert between common volume units before entering a value.
| From | To cm³ | To in³ | To liters |
|---|---|---|---|
| 1 mL | 1 | 0.061 | 0.001 |
| 1 L | 1,000 | 61.024 | 1 |
| 1 in³ | 16.387 | 1 | 0.0164 |
| 1 ft³ | 28,316.8 | 1,728 | 28.317 |
| 1 US gal | 3,785.4 | 231 | 3.785 |
Quick cube-side check for one cube (N = 1): a known volume gives one fixed side length.
| Cube volume | Side length |
|---|---|
| 1 cm³ | 1 cm |
| 27 cm³ | 3 cm |
| 125 cm³ | 5 cm |
| 1,000 cm³ (1 L) | 10 cm |
| 1 m³ | 1 m |
| 1 ft³ | 12 in |
Worked Examples
Cube. A cube holds 64 cm³. Side = ∛64 = 4 cm.
Box. A box has volume 240 cm³ with two known sides of 8 cm and 5 cm. Missing side = 240 ÷ (8 × 5) = 6 cm.
Cylinder height. A 500 mL cylinder (500 cm³) has a 10 cm diameter, so r = 5 cm. Height = 500 ÷ (π × 25) ≈ 6.366 cm.
Cylinder diameter. A 500 cm³ cylinder is 8 cm tall. Diameter = 2 × √(500 ÷ (π × 8)) ≈ 8.92 cm.
Why does mixing units fail? Volume scales with the cube of length. If you enter volume in cm³ but a known side in inches, the formula gives a meaningless answer unless the units are converted first. The calculator handles this automatically as long as you pick the correct unit next to each field.
