Metric conversions multiply by 10, 100 or 1000 for a smaller unit and divide for a larger one. Area and volume need extra care: because 1 m = 100 cm, 1 m² = 100² = 10 000 cm² and 1 m³ = 100³ = 1 000 000 cm³. Compound units such as km/h or g/cm³ are converted one part at a time.
Conversion factors
- 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm
- 1 m² = 10 000 cm², 1 cm² = 100 mm²
- 1 m³ = 1 000 000 cm³, 1 cm³ = 1000 mm³
- 1 litre = 1000 cm³, so 1 m³ = 1000 litres
- km/h to m/s: ÷ 3.6
Length, mass and capacity
To convert to a smaller unit, multiply; to convert to a larger unit, divide. 4.7 km = 4700 m, because there are 1000 m in a kilometre. Mass and capacity work the same way: 1 kg = 1000 g and 1 litre = 1000 ml.
Converting area
An area unit is a length unit squared, so square the length conversion factor. 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm². That means 0.8 m² = 8000 cm², and 7 cm² = 700 mm², because 1 cm² = 10 × 10 = 100 mm². Using 100 instead of 10 000 for m² to cm² is the most common error.
Converting volume and capacity
A volume unit is a length unit cubed, so cube the factor: 1 m³ = 100³ = 1 000 000 cm³. Volume links to capacity through 1 litre = 1000 cm³. So 0.25 m³ = 250 000 cm³, which is 250 litres.
Converting compound units
Convert each part of a compound unit separately. To change 54 km/h to m/s, change kilometres to metres (× 1000) and hours to seconds (÷ 3600), which together divide by 3.6: 54 ÷ 3.6 = 15 m/s. Density of 2.4 g/cm³ is 2400 kg/m³.
Conversions in problems
Many questions need a conversion before you can compare or calculate, such as finding how many 250 ml cups fill a 2 litre bottle. Put everything in the same unit first, then carry out the calculation.
Worked examples
Example 1. Convert 4.7 km into metres.
- 1 km = 1000 m, so multiply by 1000.
Answer: 4700 m.
Example 2. Convert 0.8 m² into cm².
- 1 m² = 10 000 cm².
- 0.8 × 10 000.
Answer: 8000 cm².
Example 3. Convert 7 cm² into mm².
- 1 cm² = 100 mm².
- 7 × 100.
Answer: 700 mm².
Example 4. A tank holds 0.25 m³ of water. Write this in cm³ and in litres.
- 0.25 × 1 000 000 = 250 000 cm³.
- 250 000 ÷ 1000 litres.
Answer: 250 000 cm³, which is 250 litres.
Example 5. Convert 54 km/h into m/s.
- Divide by 3.6: 54 ÷ 3.6.
Answer: 15 m/s.
Common mistakes
- Using 100 for m² to cm². 1 m² = 10 000 cm², because 100 is squared.
- Using 1000 for m³ to cm³. 1 m³ = 1 000 000 cm³, because 100 is cubed.
- Dividing when you should multiply. Changing to a smaller unit gives a bigger number.
- Converting only one part of a compound unit. Convert both the distance and the time units.
- Confusing cm³ and litres. 1 litre = 1000 cm³.
How unit conversion is examined
Simple conversions appear at Foundation and Higher on 1MA1 and 4MA1 papers, while area, volume and compound unit conversions are more common at Higher. Questions ask you to:
- convert metric units of length, mass and capacity
- convert units of area and volume
- link volume to capacity in litres
- convert compound units such as km/h to m/s
The converting units worksheet has questions with answers, and the GCSE proportion revision engine gives more practice.
For everyday metric units and time, see standard units and measures. Volume conversions are used in volume and surface area.
Frequently asked questions
How many cm² are in a m²?
10 000, because 1 m = 100 cm and 100² = 10 000.
How many cm³ are in a m³?
1 000 000, because 100³ = 1 000 000.
How many litres are in a cubic metre?
1000 litres.