To work out the volume of a cuboid or rectangular box, multiply length × width × height. For a cube, cube the side length. For a cylinder, multiply π × radius² × height. The result is in cubic units. To convert cubic metres to litres, multiply by 1,000. A 6 m³ tank holds 6,000 litres.
Use the volume calculator for boxes, cylinders, spheres, cones, capsules and eight other shapes, with output in m³, litres, gallons and cubic feet. Every formula below is worked through with a numbered example.
How Do You Calculate the Volume of a Cuboid or Rectangular Box?
A cuboid — also called a rectangular box or rectangular prism — is the most common shape in construction and storage. The volume is the product of its three dimensions.
Formula: V = L × W × H
Worked example: A box measures 2 m long, 1.5 m wide and 1 m high. V = 2 × 1.5 × 1 = 3 m³. The same box in centimetres is 200 cm × 150 cm × 100 cm, giving 3,000,000 cm³ — the same volume, different unit.
| Length | Width | Height | Calculation | Volume |
|---|---|---|---|---|
| 2 m | 1.5 m | 1 m | 2 × 1.5 × 1 | 3 m³ |
| 4 m | 2 m | 0.75 m | 4 × 2 × 0.75 | 6 m³ |
| 6 m | 5 m | 4.5 m | 6 × 5 × 4.5 | 135 m³ |
| 30 cm | 20 cm | 15 cm | 30 × 20 × 15 | 9,000 cm³ |
The volume of a box calculator handles any unit combination and returns the result in eight units without manual conversion.
How Do You Work Out the Volume of a Cube?
A cube is a cuboid with all three dimensions equal. The formula collapses from L × W × H to side × side × side, written as a³.
Formula: V = a³
Worked example: A cube with 2 m sides: V = 2 × 2 × 2 = 8 m³. A cube with 3 m sides: V = 27 m³. The volume of a cube calculator takes a single side length and returns all eight units.
How Do You Work Out the Volume of a Cylinder?
A cylinder is a circular base extended through a height. The volume is the area of the circular base multiplied by the height.
Formula: V = π × r² × h
Worked example: A cylinder with radius 0.5 m and height 2 m: V = 3.1416 × 0.25 × 2 = 1.571 m³, or 1,571 litres. If the diameter is given as 1 m, the radius is 0.5 m. The volume of a cylinder calculator accepts radius or diameter.
For a cylinder where the diameter is known but the radius is not: r = d ÷ 2. For a half-cylinder: divide the result by two. For a hollow cylinder (tube): subtract the inner volume from the outer volume.
How Do You Convert Cuboid Volume to Litres?
Litres are a measure of capacity, not a separate volume formula. The conversion depends on the unit of the cubic result.
| If volume is in | Multiply by | To get litres |
|---|---|---|
| Cubic metres (m³) | 1,000 | Litres (L) |
| Cubic centimetres (cm³) | 1 | Millilitres (mL), or litres ÷ 1,000 |
| Cubic millimetres (mm³) | 0.001 | Millilitres (mL), or litres ÷ 1,000,000 |
| Cubic feet (ft³) | 28.3168 | Litres (L) |
| Cubic inches (in³) | 0.0163871 | Litres (L) |
Worked example: A cuboid tank measures 4 m × 2 m × 0.75 m. Volume = 4 × 2 × 0.75 = 6 m³. In litres: 6 × 1,000 = 6,000 L.
A smaller container measuring 85 cm × 65 cm × 20 cm gives 110,500 cm³. Since 1,000 cm³ = 1 litre, 110,500 ÷ 1,000 = 110.5 litres.
The cuboid volume calculator returns litres directly when the dimensions are entered in metres or centimetres — no manual conversion step.
How Do You Calculate the Volume of Water in a Cuboid Container?
Water volume inside a cuboid container uses the same formula, with one difference: the height is the water depth, not the full container height. The internal dimensions matter, not the external ones.
Worked example: A container has internal dimensions 6 m × 5 m, and the water stands 4.5 m deep. Water volume = 6 × 5 × 4.5 = 135 m³. In litres: 135 × 1,000 = 135,000 L.
If the container is not full, use the water depth. If the container has sloped sides, the shape is a frustum, not a cuboid — use the frustum formula or the volume calculator on the frustum tab.
What Is the Rectangular Prism Volume Formula?
A rectangular prism is the same shape as a cuboid. The formula is identical: V = l × w × h, where l is length, w is width, and h is height.
The volume of a rectangular prism calculator uses the same three dimensions. The terms differ by region: “cuboid” is more common in British and Commonwealth usage, “rectangular prism” in American textbooks. The arithmetic does not change.
Worked example: A prism with length 5 cm, width 3 cm and height 2 cm: V = 5 × 3 × 2 = 30 cm³. The same prism in metres is 0.05 × 0.03 × 0.02 = 0.00003 m³ — 30 cm³ expressed in cubic metres.
When Should You Use a Volume Calculator?
The manual formulas are simple for a single shape. A calculator earns its place when one of four conditions appears:
- Mixed units. A box measured in metres and centimetres cannot be multiplied until both are in the same unit. The volume calculator normalises the units before multiplying.
- Litres and gallons at the same time. A tank quote may need cubic metres, litres, and US or UK gallons on the same page. The calculator returns all eight units from one set of dimensions.
- Weight from volume. Once the volume is known, a material density converts it to weight. The calculator includes a material selector and returns total weight.
- Irregular shapes. A capsule, a frustum, or an ellipsoid has a formula that is easy to mis-remember. The volume of a box calculator covers twelve shapes, including the ones with no single side-cubed shortcut.
The Mistakes That Break Volume Calculations
- Mixing units before multiplying. 2 m × 150 cm × 1 m produces 300, not 3. Convert every dimension to the same unit first.
- Using diameter as radius. The cylinder formula uses radius. A diameter of 1 m means a radius of 0.5 m — using 1 m in the formula quadruples the result.
- Using external dimensions for capacity. A tank's wall thickness reduces the internal volume. Measure inside faces for water capacity.
- Forgetting the litres conversion. A volume in cubic metres is not a volume in litres. The factor is 1,000, not 100 or 10.
- Assuming a cube when the sides differ. A “2 m cube” that is actually 2 m × 1.9 m × 2.1 m is not 8 m³ — it is 7.98 m³, and the difference matters at scale.