Background reading · Mathematics and Statistics

Squared and cubed: area, volume and litres

Why area is measured in square units and volume in cubic units, how litres connect to cubes, and what happens when you scale a design up.

Perimeter, area and volume all measure a space, but in different ways. Mixing them up is one of the most common, and most expensive, mistakes people make.

Three ways to measure a space

Perimeter: the distance around the edge, in metres. It tells you how much timber a garden bed needs, or how much fencing goes around a field.

Area: the space covered, in square units (m²). A rectangle's area is length × width. It tells you how much garden you can plant, or how much carpet you need.

Volume: the space inside, in cubic units (m³). A box's volume is length × width × height. It tells you how much soil fills a bed or how much water a tank holds.

From cubes to litres

A cube 10 cm on each side has a volume of 10 × 10 × 10 = 1000 cm³, and it holds exactly 1 litre. So 1 mL = 1 cm³. A cube 1 m on each side holds 1000 of those small cubes: 1 m³ = 1000 litres. A raised bed 2.4 m long, 1.2 m wide and 0.3 m deep holds 2.4 × 1.2 × 0.3 = 0.864 m³, which is 864 litres of soil, or 22 bags of 40 litres.

Rain on the roof

Here is a handy fact: 1 mm of rain falling on 1 m² of roof is 1 litre of water. A 100 m² classroom roof in a 20 mm downpour collects 100 × 20 = 2000 litres. That is why water tanks fill so fast in a storm.

The scaling surprise

What happens if you double every length of a design? The perimeter doubles. But the area becomes 4 times bigger (2 × 2), and the volume becomes 8 times bigger (2 × 2 × 2). A garden bed twice as long, twice as wide and twice as deep needs eight times the soil. Designers who forget this order far too little, or build something far too heavy.

Sources and further reading

Written for Kōkiri Learn students in our own words. Check facts against the sources.

Used in: Measure Up: Designing Spaces