Calculate cube side, missing box side, or cylinder height or diameter from known volume, using metric or imperial units and return lengths in cm to yd.
Reverse Volume Formula
The calculator solves for a missing dimension when you already know the volume. The formula depends on the shape.
Cube: s = ∛V
Box: c = V / (a × b)
Cylinder: h = V / (π × r²)
d = 2 × √(V / (π × h))- V = known volume
- s = cube side length
- a, b = known box sides; c = missing box side
- r = cylinder radius; d = diameter; h = height
All inputs must use consistent units before the formula is applied. The calculator converts every entry to cubic meters and meters internally, then converts the answer back to the unit you select. Volume must be greater than zero, and for the box mode both known sides must be greater than zero.
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: 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.
