Convert units of length, area, volume and capacity
Choose the right metric conversion factor for length, mass, area, volume and capacity, including squared and cubed units.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many metres are in 1 km?
What you will learn
- Convert metric units in practical situations
- Convert squared and cubed units using scale factors
- Relate cubic metres to litres and keep units with answers
Convert one dimension at a time
For length, each metric step scales by 10, 100 or 1000 as appropriate: 1 km = 1000 m and 1 m = 100 cm. For mass, 1 kg = 1000 g.
For area, square the length factor: 1 m² = 100² cm² = 10 000 cm². For volume, cube it: 1 m³ = 100³ cm³ = 1 000 000 cm³.
Capacity is a volume measure
1 litre = 1000 ml and 1 m³ = 1000 litres. Also 1 cm³ = 1 ml. Convert to a common unit before adding or comparing quantities.
Write the units in each step so a factor is not accidentally applied once when the dimension is squared or cubed.
Pause and explain
What length factor must be squared to convert m² to cm²?
Worked example
Convert 2.4 km to metres, 3500 cm² to m², and 0.004 m³ to litres.
Show the worked solution
- 2.4 km = 2.4 × 1000 = 2400 m.
- 3500 cm² ÷ 10 000 = 0.35 m².
- 0.004 m³ × 1000 = 4 litres.
Answer 2400 m; 0.35 m²; 4 litres.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 3.6 kg to grams, 0.45 m² to cm², and 2.5 litres to millilitres.
Give me a hint
Use 1000 for kg-to-g and L-to-ml; square 100 for m²-to-cm².
Compare my reasoning
- 3.6 kg = 3600 g.
- 0.45 m² × 10 000 = 4500 cm².
- 2.5 litres = 2500 ml.
3600 g; 4500 cm²; 2500 ml.
Look for these in your work
- Mass factor correct
- Area factor squared
- Capacity factor correct
A tank holds 0.75 m³ of water. Convert this to litres and then to millilitres.
Give me a hint
Use 1000 litres per cubic metre and 1000 millilitres per litre.
Compare my reasoning
- 0.75 m³ × 1000 = 750 litres.
- 750 × 1000 = 750 000 ml.
- Keep the unit chain explicit.
750 litres; 750 000 ml.
Look for these in your work
- Volume-to-capacity conversion
- Litre-to-millilitre conversion
- Units retained
A tile is 25 cm by 40 cm. Find its area in m² and the area of 24 such tiles in m².
Give me a hint
Find one area in cm², then convert using 10 000 cm² per m².
Compare my reasoning
- One tile area = 25 × 40 = 1000 cm².
- 24 tiles cover 24 000 cm².
- 24 000 ÷ 10 000 = 2.4 m².
One tile 0.1 m²; 24 tiles 2.4 m².
Look for these in your work
- Area calculated
- Tile count applied
- Square-unit conversion used
Common mistakes
- Using a length conversion factor unchanged for area or volume
- Moving the decimal in the wrong direction
- Adding litres to cubic centimetres without conversion
- Dropping squared or cubed unit notation
What can you explain now?
How many square centimetres are in 1 m²?
Compare with the explanation
10 000 cm²
Square the 100 centimetres in one metre.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Why do area and volume conversions square or cube the length factor?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.