Free GCSE Maths lesson: Geometry and Measures
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Lesson 45 · GCSE / Key Stage 4 · Maths · Geometry and Measures

Units, Metric Conversions and Measures

Learn how to convert metric units without losing place value, and how to choose sensible units for GCSE measure questions.

Qualification: GCSE Key Stage 4 Subject: Maths Strand: Geometry and Measures

GCSE specification fit

Unit conversions are a place-value skill, not a guessing skill.

GCSE Maths questions often hide a unit conversion inside area, volume, scale, speed, density, pressure or real-life measure work. The safest habit is to write the conversion fact, decide whether you are converting length, area or volume, then keep the unit attached to the number.

QualificationGCSE Mathematics
Key stageKey Stage 4
StrandGeometry and Measures
Tier guidanceFoundation and Higher

What you will learn

  • How to convert between mm, cm, m and km.
  • How to convert between g, kg, ml and litres.
  • Why area and volume conversions use squared and cubed factors.
  • How to read measured values from a scale.
  • How to spot whether an answer unit is sensible.
  • How to use conversions inside geometry, capacity and rate questions.

Why this matters

Unit errors can make a correct method look wrong. In exams, conversions appear in questions about maps, packaging, recipes, construction, travel, liquids and compound measures, so confident unit work protects marks across several topics.

Prior knowledge

You should already be comfortable with:

  • multiplying and dividing by 10, 100 and 1000,
  • moving between decimals and whole numbers,
  • using area units such as cm² and m²,
  • using volume and capacity units such as cm³, m³, ml and litres.

Clear explanation

Common metric facts

These are the conversion facts that appear most often. Write the one you need before doing the calculation.

10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km 1000 g = 1 kg 1000 ml = 1 litre

Length conversions

When the unit gets smaller, the number gets bigger because you need more smaller units to make the same measurement. When the unit gets bigger, the number gets smaller.

3.6 m = 3.6 × 100 = 360 cm 4500 m = 4500 ÷ 1000 = 4.5 km

Area and volume conversions

Area is two-dimensional, so both length directions change. Since 1 m = 100 cm, one square metre is 100 cm by 100 cm.

1 m² = 10 000 cm²

Volume is three-dimensional, so three directions change.

1 m³ = 1 000 000 cm³

This is why you must not use the same multiplier for cm, cm² and cm³.

Capacity and volume links

Capacity questions may connect litres, millilitres and cubic centimetres. A useful GCSE fact is that 1 cm³ holds 1 ml, so 1000 cm³ holds 1000 ml, which is 1 litre.

1 cm³ = 1 ml 1000 cm³ = 1 litre

Conversions inside longer questions

Many exam questions do not say "convert" in the first sentence. If a length is in metres but an area must be in cm², or a volume is in cm³ but the answer asks for litres, convert before comparing, substituting or rounding.

Worked examples

Example 1: Convert metres to centimetres

Convert 2.75 m into centimetres.

1 m = 100 cm 2.75 m = 2.75 × 100 = 275 cm
Answer: 275 cm.

Example 2: Convert grams to kilograms

Convert 640 g into kilograms.

1000 g = 1 kg 640 g = 640 ÷ 1000 = 0.64 kg
Answer: 0.64 kg.

Example 3: Convert square metres to square centimetres

Convert 0.35 m² into cm².

1 m² = 10 000 cm² 0.35 m² = 0.35 × 10 000 = 3500 cm²
Answer: 3500 cm².

Quick checks

Choose an answer, then check your thinking.

1. 5.4 m is:

2. 2300 g is:

3. 1 m² is:

Practice questions

Question 1

Convert 4.8 km into metres.

Reveal answer and marking guidance

Answer: 4800 m.

Marking: Use 1 km = 1000 m, then 4.8 × 1000 = 4800.

Question 2

Convert 76 mm into centimetres.

Reveal answer and marking guidance

Answer: 7.6 cm.

Marking: Use 10 mm = 1 cm, then 76 ÷ 10 = 7.6.

Question 3

Convert 0.45 kg into grams.

Reveal answer and marking guidance

Answer: 450 g.

Marking: Use 1 kg = 1000 g, then 0.45 × 1000 = 450.

Question 4

Convert 2.5 litres into millilitres.

Reveal answer and marking guidance

Answer: 2500 ml.

Marking: Use 1 litre = 1000 ml, then 2.5 × 1000 = 2500.

Question 5

Convert 3.2 m² into cm².

Reveal answer and marking guidance

Answer: 32 000 cm².

Marking: Use 1 m² = 10 000 cm², then 3.2 × 10 000 = 32 000.

Question 6

A container holds 18 500 cm³ of water. How many litres is this?

Reveal answer and marking guidance

Answer: 18.5 litres.

Marking: Use 1000 cm³ = 1 litre, then 18 500 ÷ 1000 = 18.5.

Question 7

Convert 0.008 m³ into cm³.

Reveal answer and marking guidance

Answer: 8000 cm³.

Marking: Use 1 m³ = 1 000 000 cm³, then 0.008 × 1 000 000 = 8000.

Question 8

A runner travels 750 m in 3 minutes. Write this speed in metres per second.

Reveal answer and marking guidance

Answer: 4.17 m/s to 3 significant figures, or exactly 4.1666... m/s.

Marking: Convert 3 minutes to 180 seconds, then use speed = distance ÷ time = 750 ÷ 180 = 4.1666... m/s.

Question 9

A cuboid tank measures 80 cm by 45 cm by 30 cm. Find its capacity in litres.

Reveal answer and marking guidance

Answer: 108 litres.

Marking: Volume = 80 × 45 × 30 = 108 000 cm³. Use 1000 cm³ = 1 litre, so 108 000 ÷ 1000 = 108 litres.

Question 10

A metal block has volume 250 cm³ and mass 1.95 kg. Find its density in g/cm³.

Reveal answer and marking guidance

Answer: 7.8 g/cm³.

Marking: Convert 1.95 kg to 1950 g first. Then density = mass ÷ volume = 1950 ÷ 250 = 7.8 g/cm³.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For unit-conversion questions, marks usually come from writing the correct conversion fact, choosing multiplication or division sensibly, keeping place value accurate, and using the final unit. For area, volume, capacity and rate questions, show the squared, cubed or time conversion before substituting into the main calculation.

Common mistakes

  • Multiplying when you should divide: think about whether the new unit is smaller or larger.
  • Using 100 for every conversion: metres to centimetres use 100, but kilometres to metres use 1000.
  • Forgetting squared units: 1 m² is 10 000 cm², not 100 cm².
  • Dropping the unit: 450 could mean grams, kilograms, millilitres or metres unless you write the unit.

Extension challenge

A rectangular garden is 8 m by 3.5 m. A plan of the garden is drawn in centimetres. Convert the garden area into cm².

Reveal answer

Answer: 280 000 cm².

The area is 8 × 3.5 = 28 m². Since 1 m² = 10 000 cm², 28 m² = 280 000 cm².

Exam-board guidance

Metric units and measures are core GCSE Maths skills across all boards. The wording may appear in pure conversion questions or inside geometry, ratio, proportion and real-life contexts.

AQA GCSE Maths

Write the conversion you are using before calculating, especially for area, volume and scale-reading questions where one missed unit can change the answer.

OCR GCSE Maths

Check whether the question is changing length, area, volume or capacity units before choosing a multiplier, then keep the unit attached.

Pearson Edexcel GCSE Maths

Expect unit conversion to appear inside longer questions, so convert before substituting into area, volume, speed, density or pressure formulae.

Eduqas GCSE Maths

Use a clear conversion line so the examiner can follow each step, including any square, cubic or capacity unit change.

WJEC Wales

Be ready to explain units in everyday contexts such as measuring instruments, capacity, mass, materials and scale, then check whether the answer is sensible.

CCEA GCSE Maths

Show the conversion factor and keep units attached in both calculator and non-calculator units, especially for area, volume and capacity problems.

Next lesson

Next, continue Geometry and Measures with Time, Money and Real-Life Measures.

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