What is the formula for the volume of a cuboid?

The volume of a cuboid is calculated by multiplying its three dimensions together: Volume = length x width x height (V = l x w x h). All three measurements must be in the same unit before multiplying. The result is expressed in cubic units, for example cubic metres (m³), cubic centimetres (cm³), or cubic feet (ft³). A cuboid is also known as a rectangular prism or rectangular box.

How do I convert the volume from cubic metres to litres?

One cubic metre equals exactly 1,000 litres. To convert, multiply your volume in m³ by 1,000. For example, a cuboid with volume 0.5 m³ holds 500 litres. Similarly, one cubic centimetre equals one millilitre, so a volume in cm³ gives you the same number of millilitres directly. This relationship is useful for calculating tank or container capacity.

What is the difference between a cube and a cuboid?

A cube is a special type of cuboid where all three dimensions (length, width and height) are equal. Every cube is a cuboid, but most cuboids are not cubes. Both have six rectangular faces, twelve edges and eight vertices. For a cube with side s, the volume formula simplifies to V = s³. For a general cuboid where the three dimensions differ, you must multiply all three separately: V = l x w x h.

Cuboid Volume Calculator

This calculator works out the volume of a cuboid, also called a rectangular box or rectangular prism, from its three straight-line dimensions. A cuboid is any solid with six flat rectangular faces, so the tool suits jobs from sizing a garden bed or water tank to estimating a shipping container, a room's air volume, or the material needed to fill a raised bed. You enter the length, width and height, then pick the unit you are measuring in: metres, centimetres, millimetres, feet or inches. The calculator applies the standard formula V = length x width x height and returns the volume instantly in your chosen unit, alongside automatic conversions to cubic metres, litres, cubic feet, cubic centimetres, cubic millimetres, cubic inches, cubic yards and millilitres, so you never need to convert units by hand. A breakdown panel repeats each dimension you entered next to the resulting volume, and a worked example using the default 5 m x 3 m x 2 m box shows exactly how the maths works, including the litre and cubic foot equivalents. Change any figure and every result updates immediately. Because it is a straightforward geometric calculation, accuracy depends entirely on how precisely you measure length, width and height, so for construction, shipping or compliance decisions, double check your measurements and treat the output as an estimate rather than a certified figure.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.

Calculate.co.nz partner: Health Based Building

Advertise on this page

Standard formula V = l x w x h. A cuboid is any solid with six rectangular faces.

1. Dimensions

Unit of measurement

Length (m)

Width (m)

Height (m)

2. Results

Volume
30
m³

Cubic Metres

m³

Litres

30,000

L (1 m³ = 1,000 L)

Cubic Feet

1,059

ft³

Volume Breakdown

Length5 m

Width3 m

Height2 m

Volume (l x w x h)30 m3

Additional Conversions

Cubic centimetres30,000,000 cm3

Cubic millimetres30,000,000,000 mm3

Cubic inches1,830,712 in3

Cubic yards39.2385 yd3

Millilitres30,000,000 mL

Worked Example (default values)

Length = 5 m, Width = 3 m, Height = 2 m

V = l x w x h = 5 x 3 x 2 = 30 m³

30 m³ = 30,000 litres = 1,059.44 ft³

How to Calculate the Volume of a Cuboid

A cuboid is a three-dimensional solid with six rectangular faces. It is also called a rectangular prism or rectangular box. The volume tells you how much space the cuboid occupies, or how much it can hold if it is a container.

The formula is straightforward:

Volume = Length x Width x Height

All three measurements must be in the same unit before you multiply. The result is in cubic units of that measurement. For example, if you measure in centimetres, the volume is in cubic centimetres (cm³).

The Formula

Symbol	Meaning	Example
V	Volume (the result)	30 m³
l	Length of the longest side	5 m
w	Width (the shorter horizontal dimension)	3 m
h	Height (vertical dimension)	2 m

V = 5 x 3 x 2 = 30 m³. This is also 30,000 litres, which is useful when sizing water tanks or swimming pools.

Common Unit Conversions

From	To	Multiply by
m³	Litres	1,000
m³	cm³	1,000,000
m³	ft³	35.3147
cm³	mL	1
ft³	Gallons (US)	7.48052
in³	cm³	16.3871

Practical Examples

Soil or mulch for a raised garden bed: A bed 2 m long, 1.2 m wide and 0.3 m deep needs 2 x 1.2 x 0.3 = 0.72 m³ (720 litres) of material.
Shipping container: A standard 20-foot ISO container is roughly 5.9 m x 2.35 m x 2.39 m = approximately 33.1 m³ internal volume.
Room air volume: A room 4 m x 3.5 m x 2.4 m has a volume of 33.6 m³. This matters for air conditioning and ventilation sizing.
Water tank: A tank 1.5 m x 1.0 m x 1.0 m holds 1.5 m³ = 1,500 litres of water.

Cuboid vs Cube

A cube is a special case of a cuboid where all three dimensions are identical. For a cube with side length s, the volume simplifies to V = s³. For a general cuboid where the three dimensions differ, you must always multiply all three values separately. This calculator handles both cases.

Surface Area vs Volume

Volume and surface area are different properties. Volume measures the space inside, while surface area measures the total area of all six faces. The surface area formula for a cuboid is SA = 2(lw + lh + wh). If you need the surface area as well, use the Rectangular Box (Cuboid) Calculator, which gives both at once.

Related Calculators

Maths and Stats Calculators: all geometry and maths tools.
Rectangular Box (Cuboid) Calculator: volume and surface area together.
Volume Calculator (multi-solid): spheres, cylinders, cones and more.
Cuboid Calculator: full cuboid properties including diagonal length.
Cube Surface Area and Volume Calculator: for perfect cubes with equal sides.

Sources and method: Volume formula V = l x w x h is a standard Euclidean geometry result. Unit conversion factors from SI (International System of Units) definitions: 1 m = 100 cm = 1,000 mm; 1 ft = 0.3048 m; 1 in = 0.0254 m. 1 m³ = 1,000 L (BIPM SI Brochure).

This calculator is for informational and educational purposes. For engineering, construction or compliance purposes, verify all measurements and calculations independently.