How to Calculate Volume in Cubic Metres (m³)

Volume measures the three-dimensional space an object or substance occupies. To calculate it in cubic metres, written as m³, you need the object’s shape and its dimensions. The correct formula depends on whether you are measuring a box, cylinder, sphere, or another shape.

The key unit rule is to use metres for every length before calculating. Since volume involves three dimensions, a conversion factor for length must also be cubed when converting a volume.

Formulas for common shapes

Use the formula that matches the object. The dimensions must be measured in the same unit.

Shape	Volume formula	Dimensions
Rectangular prism or box	$V = lwh$	length $l$, width $w$, height $h$
Cube	$V = s^3$	side length $s$
Cylinder	$V = \pi r^2h$	radius $r$, height $h$
Sphere	$V = \frac{4}{3}\pi r^3$	radius $r$

If the measurements are in metres, the result is in cubic metres. For example, multiplying three metre measurements gives units of $\text{m} \times \text{m} \times \text{m} = \text{m}^3$.

Worked example: rectangular room

Suppose a room is 4.2 m long, 3 m wide, and 2.5 m high. Treating it as a rectangular prism:

$$\begin{aligned} V &= lwh \\ &= 4.2 \times 3 \times 2.5 \\ &= 31.5\ \text{m}^3 \end{aligned}$$

The room’s volume is 31.5 m³. This is the space inside the room, assuming its walls and ceiling form a rectangular prism.

If your measurements are in centimetres

Convert each dimension to metres before using the formula, or calculate in cubic centimetres and convert the final answer. Because $1\ \text{m} = 100\ \text{cm}$:

$$1\ \text{m}^3 = 100^3\ \text{cm}^3 = 1{,}000{,}000\ \text{cm}^3$$

For example, a box measuring 200 cm by 150 cm by 80 cm can be converted to 2 m by 1.5 m by 0.8 m. Then:

$$V = 2 \times 1.5 \times 0.8 = 2.4\ \text{m}^3$$

Alternatively, its volume is $200 \times 150 \times 80 = 2{,}400{,}000\ \text{cm}^3$. Dividing by 1,000,000 gives $2.4\ \text{m}^3$.

Other useful conversions are:

• $1\ \text{m}^3 = 1{,}000\ \text{L}$
• $1\ \text{L} = 0.001\ \text{m}^3$
• $1\ \text{cm}^3 = 0.000001\ \text{m}^3$

For instance, a 500 L tank holds $500 \div 1{,}000 = 0.5\ \text{m}^3$.

Worked example: cylindrical tank

A vertical cylindrical tank has an inside radius of 0.6 m and an inside height of 1.8 m. Apply the cylinder formula, using the radius rather than the diameter:

$$\begin{aligned} V &= \pi r^2h \\ &= \pi(0.6)^2(1.8) \\ &= 0.648\pi \\ &\approx 2.04\ \text{m}^3 \end{aligned}$$

The tank’s full geometric capacity is about 2.04 m³, or about 2,040 L. The amount it actually holds will be lower if it is not filled to the top.

Irregular or combined shapes

For an object made from simple parts, split it into shapes, calculate each part’s volume, and add the results. For a hollow object, subtract the hollow space from the outer volume if you need the volume of the material itself.

For an irregular solid that cannot be divided conveniently, water displacement can give its volume. Submerge it in a graduated container and subtract the starting water volume from the final volume. Since 1 L equals 0.001 m³, convert the measured litres to cubic metres by dividing by 1,000.

Common mistakes

• Mixing units: Do not multiply a length in centimetres by a width in metres. Convert all lengths to one unit first.
• Converting the length factor only: Since volume is three-dimensional, 1 m³ is 1,000,000 cm³, not 100 cm³.
• Using diameter as radius: For a cylinder or sphere, the radius is half the diameter.
• Using the wrong dimensions: A box’s volume uses three perpendicular dimensions; its surface area is a different calculation.
• Confusing volume with mass: Volume is space occupied. To find mass, you also need the material’s density.

If you know the shape and its dimensions, a volume calculator can perform the arithmetic; check that the input units and displayed output units match your measurements.