Units of measure.
Convert lengths, areas, volumes, capacities and masses without losing the meaning of the unit.
Use metric units · square and cube conversion factors · connect litres and cubic units
Choose the quantity before the conversion
A measurement combines a number with a unit. The number alone does not tell us the size: 5 millimetres and 5 kilometres describe very different lengths.
Metric units are linked by fixed factors. Changing the unit does not change the actual object; it changes how many unit-sized pieces are needed to describe it. Predict whether the numerical value should increase or decrease before choosing multiplication or division.
Length, area and volume measure different things. Their units show how many dimensions are involved. Mass and capacity have their own conversion relationships.
| Quantity | Useful conversions | Typical use |
|---|---|---|
| Length | 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km | Distance, height, perimeter |
| Area | 100 mm² = 1 cm²; 10 000 cm² = 1 m²; 1 000 000 m² = 1 km² | Flooring, land, surface area |
| Volume | 1000 mm³ = 1 cm³; 1 000 000 cm³ = 1 m³ | Space occupied |
| Capacity | 1000 ml = 1 litre; 1 ml = 1 cm³; 1 litre = 1000 cm³ | Liquid a container holds |
| Mass | 1000 g = 1 kg | Mass of materials |
Pause and explainWill the number increase when 2 metres is written in centimetres?
Yes. Centimetres are smaller units, so 200 of them are needed to describe the same length.
Square and cube the length factor
An area counts square units and a volume counts cube units. Changing the length of one unit changes more than one dimension of these small measuring pieces.
Since 1 m = 100 cm, a 1 m by 1 m square contains 100 × 100 square centimetres. A cubic metre contains 100 × 100 × 100 cubic centimetres. This is why length conversion factors must be squared for area and cubed for volume.
The conversion is applied to each of two dimensions. To convert back, divide by the same factor.
Convert 2.4 m² to cm² and 750 cm² to m².
2.4 × 10 000 = 24 000 cm².
750 ÷ 10 000 = 0.075 m².
Convert 0.035 m³ to litres and 450 ml to cm³.
0.035 × 1000 = 35 litres. Also, 450 ml = 450 cm³.
Pause and explainWhy is 1 m² not equal to 100 cm²?
Both dimensions change by 100, so the area factor is 100² = 10 000.
Convert before substituting
Choose units suited to the object and the required calculation. A person’s mass is naturally described in kilograms, a small medicine dose in millilitres, and a room’s floor area in square metres.
Capacity and volume are different descriptions of space that can be converted. Use a known bridge such as 1 litre = 1000 cm³ rather than inventing a new decimal movement. When a formula combines measurements, convert its inputs to consistent units before substituting.
A tank measures 80 cm by 50 cm by 0.6 m. Find its capacity in litres.
First convert 0.6 m to 60 cm.
Capacity = 240 000 ÷ 1000 = 240 litres
Using 80 × 50 × 0.6 would mix units and give an incorrect result.
A bag has mass 2.35 kg. How many 50 g portions can be made?
2350 ÷ 50 = 47 portions
Pause and explainWhy convert 50 cm to metres before multiplying it by 2 m for an area in m²?
The two dimensions need the same length unit. Use 0.5 m × 2 m = 1 m².
Your turn. Track the unit power.
Write the starting and target units beside each conversion. Decide whether the quantity is a length, area, volume, capacity or mass.
Use the correct factor for that dimension and predict whether the numerical answer should grow or shrink. A sketch of a square or cube can explain a factor that otherwise seems easy to forget.
Convert 3.6 km to metres and 0.045 kg to grams.
Reveal worked answer
Convert 0.08 m² to cm² and 2500 mm² to cm².
Reveal worked answer
Convert 1.25 m³ to litres and 3200 cm³ to litres.
Reveal worked answer
A container is 30 cm by 20 cm by 25 cm. Find its capacity in litres.