🧊 Volume Calculator
Find the volume of a cube, box, cylinder, sphere, cone or pyramid and convert it to litres and US gallons.
Quick answer: Volume of a box = length × width × height, so a 30 cm × 20 cm × 10 cm box holds 6,000 cm³ – exactly 6 litres, because 1,000 cm³ = 1 L.
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Volume Calculator inputs
Result
Volume of the rectangular prism (box)
6,000 cm³
= 6 litres
- Formula
- V = length × width × height
- Litres
- 6 L
- US gallons
- 1.585 gal
- Cubic metres
- 0.006 m³
Working
- Use the formula V = length × width × height
- Substitute: V = 30 × 20 × 10
- V = 6,000 cm³
- Convert: 1 cm³ = 0.001 L, so V = 6 L
Volume formulas
Volume is the amount of three-dimensional space a solid occupies, measured in cubic units (cm³, m³, ft³) or in capacity units such as litres and gallons.
| Shape | Formula |
|---|---|
| Cube | side³ |
| Rectangular prism (box) | length × width × height |
| Cylinder | π × r² × h |
| Sphere | ⁴⁄₃ × π × r³ |
| Cone | ⅓ × π × r² × h |
| Rectangular pyramid | ⅓ × length × width × height |
Prism or cylinder: V = base area × height · Cone or pyramid: V = ⅓ × base area × height
Worked examples
- Box: 30 × 20 × 10 cm = 6,000 cm³ = 6 litres.
- Cylinder: radius 4 cm, height 10 cm → π × 16 × 10 ≈ 502.6548 cm³.
- Sphere: radius 3 m → ⁴⁄₃ × π × 27 ≈ 113.0973 m³.
Converting volume units
Because volume has three dimensions, unit conversions are cubed. One metre is 100 cm, so one cubic metre is 100³ = 1,000,000 cm³. The calculator converts automatically to litres, US gallons and cubic metres.
| Unit | Litres |
|---|---|
| 1 cm³ | 0.001 |
| 1 in³ | 0.016387 |
| 1 ft³ | 28.317 |
| 1 m³ | 1,000 |
| 1 US gallon | 3.785 |
Tips
- Measure all dimensions in the same unit before calculating.
- For tanks and containers, use inside measurements to get the true capacity.
- If you know a diameter, halve it to get the radius.
- For irregular objects, split them into simpler solids, or measure the water they displace when submerged.
- Doubling every dimension multiplies the volume by eight, because volume grows with the cube of the scale.
Frequently asked questions
How do I convert cubic centimetres to litres?
Divide by 1,000: one litre is exactly 1,000 cm³ (a 10 cm cube). One cubic metre is 1,000 litres, and one cubic foot is about 28.317 litres.
How much water does a cylindrical tank hold?
Use V = πr²h with the inside radius and height. A tank 50 cm in radius and 120 cm tall holds π × 2,500 × 120 ≈ 942,478 cm³, or about 942 litres.
Why is a cone one third of a cylinder?
A cone with the same base and height as a cylinder fills exactly one third of it – a result that can be proved with calculus or shown by pouring. The same ⅓ factor links a pyramid to a prism.
How do I calculate cubic feet for shipping or concrete?
Measure length, width and height in feet and multiply. A slab 10 ft × 10 ft × 4 in (0.333 ft) needs about 33.3 cubic feet, or 1.23 cubic yards of concrete.