Convert between metric units of length, area and volume, and use approximate metric–imperial conversions. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Length conversions use 10, 100, 1000. Area conversions use those factors squared: 1 m² =100×100=10000 cm², not 100 cm². Volume uses cubes: 1 m³ =1000000 cm³. Forgetting to square or cube the scale factor is the error this topic exists to catch.
A diagram in cm that needs an answer in m² must be converted either before you compute the area (change each length) or after (change the cm²). Do not mix: one length in cm and one in m inside the same formula.
Length is × or ÷ 10, 100, 1000. Area is the square of that factor (1 cm² = 100 mm²). Volume is the cube (1 m³ = 1 000 000 cm³). Imperial estimates (5 miles ≈ 8 km) are a separate 1–2 mark skill.
Objectives
1 km = 1000 m. 1 m = 100 cm. 1 cm = 10 mm.
To go to a smaller unit, multiply.
1.2 m in mm is 1.2 × 100 = 120 cm, then × 10 = 1200 mm.
Key points
Convert lengths: mm, cm, m, km.
Convert area units by squaring the length factor.
Convert volume units by cubing the length factor, and link cm³ to litres.
Use approximate conversions such as 5 miles ≈ 8 km and 1 kg ≈ 2.2 pounds.
Worked examples
Example 1
How many metres are in 2 kilometres?
2 marks
1 kilometre is 1000 metres.
2 × 1000 = 2000.
2 km is 2000 m.
Answer: 2000 m
Common slips
Slip: 1 kilometre is 100 metres. There are 1000 metres in a kilometre.
Slip: 2 × 100 = 200. That uses the wrong conversion factor.
Slip: 2 km is 200 m. The answer is 10 times too small.
Example 2
How many centimetres are in 3 metres?
2 marks
1 metre is 100 centimetres.
3 × 100 = 300.
3 m is 300 cm.
Answer: 300 cm
Common slips
Slip: 1 metre is 10 centimetres. A metre is 100 centimetres, not 10.
Slip: 3 × 10 = 30. That uses the wrong conversion factor.
Slip: 3 m is 30 cm. The answer is 10 times too small.
Example 3
How many millimetres are in 4 centimetres?
3 marks
1 centimetre is 10 millimetres.
4 × 10 = 40.
4 cm is 40 mm.
Answer: 40 mm
Common slips
Slip: 1 centimetre is 100 millimetres. A centimetre is 10 millimetres, not 100.
Slip: 4 × 100 = 400. That uses the wrong conversion factor.
Slip: 4 cm is 400 mm. The answer is 10 times too big.
Questions and answers
GCSE Maths conversions & units questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
How many metres are in 200 centimetres?
Show answer
Answer: 2 m
100 centimetres make 1 metre, so divide by 100.
200 ÷ 100 = 2.
M1 — 100 centimetres make 1 metre, so divide by 100.
A1 — Answer 2 m
Question 2 Easy2 marks
How many metres are in 6 kilometres?
Show answer
Answer: 6000 m
1 kilometre is 1000 metres.
6 × 1000 = 6000.
M1 — 1 kilometre is 1000 metres.
A1 — Answer 6000 m
Question 3 Medium2 marks
How many metres are in 300 centimetres?
Show answer
Answer: 3 m
100 centimetres make 1 metre, so divide by 100.
300 ÷ 100 = 3.
M1 — 100 centimetres make 1 metre, so divide by 100.
A1 — Answer 3 m
Question 4 Medium2 marks
How many metres are in 10 kilometres?
Show answer
Answer: 10000 m
1 kilometre is 1000 metres.
10 × 1000 = 10000.
M1 — 1 kilometre is 1000 metres.
A1 — Answer 10000 m
Question 5 Hard2 marks
How many metres are in 400 centimetres?
Show answer
Answer: 4 m
100 centimetres make 1 metre, so divide by 100.
400 ÷ 100 = 4.
M1 — 100 centimetres make 1 metre, so divide by 100.
A1 — Answer 4 m
Question 6 Hard2 marks
How many metres are in 14 kilometres?
Show answer
Answer: 14000 m
1 kilometre is 1000 metres.
14 × 1000 = 14000.
M1 — 1 kilometre is 1000 metres.
A1 — Answer 14000 m
Question 7 Exam-style2 marks
How many metres are in 500 centimetres?
Show answer
Answer: 5 m
100 centimetres make 1 metre, so divide by 100.
500 ÷ 100 = 5.
500 cm is 5 m.
M1 — 100 centimetres make 1 metre, so divide by 100.
A1 — Answer 5 m
Common mistakes
Most lost marks on this topic are one slip.
Dividing when changing to a smaller unit.
Smaller units mean a larger number. Multiply.
Using 100 for metres to millimetres.
That jump is 1000.
Converting area by the length factor once.
Square the conversion.
Spot the slip
How many centimetres are in 1 metre?
100
10
1000
Show the slip
100 A metre is 100 centimetres.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the conversion fact (1 m² = 10,000 cm²) as your first line — that is the method mark.
Draw a quick 1 m by 1 m square and label it 100 cm by 100 cm if you forget the area factor.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.