How volume is calculated
Each shape has its own formula, but most are a base area times a height.
Box V = l × w × h · Cylinder V = πr²h · Sphere V = 4/3 πr³
- Cube: V = s³. Box: V = l × w × h.
- Cylinder: V = πr²h. Cone: V = ⅓πr²h. Square pyramid: V = ⅓ × base² × h.
- Sphere: V = 4/3 πr³. Hemisphere: half of that, 2/3 πr³.
- Triangular prism: V = ½ × base × height × length. Capsule: a cylinder plus a sphere, πr²L + 4/3 πr³.
- Tube or pipe: the outer cylinder minus the hollow, V = π(R² − r²) × L.
- Litres come from the cubic size: 1 m³ = 1,000 L and 1,000 cm³ = 1 L.
Worked example — A box 2 m long, 3 m wide and 4 m high: V = 2 × 3 × 4 = 24 m³, which holds 24,000 litres.
Common volumes
| Shape | Size | Volume | Litres |
|---|---|---|---|
| Cube | Side 10 cm | 1,000 cm³ | 1 L |
| Rectangular prism (box) | 2 × 3 × 4 m | 24 m³ | 24,000 L |
| Cylinder | r 50 cm, h 100 cm | 785,398.16 cm³ | 785.4 L |
| Sphere | r 10 cm | 4,188.79 cm³ | 4.19 L |
| Cone | r 3 cm, h 10 cm | 94.25 cm³ | 0.09 L |
| Square pyramid | Base 230 m, h 146 m (Great Pyramid, approx.) | 2,574,466.67 m³ | 2,574,466,666.67 L |
Swipe the table sideways to see the rest.
Each row is worked out with the same formulas as the calculator.
Things to consider
- Use the same unit for every measurement before you start.
- For a tank, use the inside measurements to find how much it holds.
- Radius is half the diameter. Measure across the middle and halve it.
- For an odd shape, split it into simple shapes and add their volumes.
Frequently asked questions
What is volume?
Volume is the amount of space a 3D object takes up, measured in cubic units such as cm³ or m³.
How do I find the volume of a box?
Multiply length × width × height. A 2 m by 3 m by 4 m box is 24 m³.
How do I convert cubic metres to litres?
Multiply by 1,000. 1 m³ = 1,000 L, so 2.5 m³ is 2,500 L.
How do I convert cm³ to mL?
They are the same. 1 cm³ = 1 mL, and 1,000 cm³ = 1 L.
How many litres does a rainwater tank hold?
Treat a round tank as a cylinder. A tank with a 1 m radius and 2 m height holds π × 1² × 2 = 6.28 m³, about 6,283 litres. The Cylinder Volume Calculator goes into more detail.
What is the difference between volume and capacity?
Volume is the space an object takes up. Capacity is how much a container can hold, usually in litres. For a thin-walled tank they are almost the same.
Results are estimates for general information only, not financial, medical or professional advice.