Unit Conversions –

Unit conversions might sound straightforward, but they catch out more GCSE students than you would expect — especially when area and volume units are involved. Every exam board (AQA, Edexcel, OCR) tests conversions in some form, from simple metric changes on Foundation papers to tricky cm² to m² conversions on Higher. Getting these right often means the difference between full marks and losing marks on an otherwise correct calculation. This guide covers the metric system, imperial approximations, area and volume conversions, and gives you worked examples and practice questions to build fluency. For a complete list of formulas to memorise, see our GCSE Maths formulas guide.

What Are Unit Conversions?

A unit conversion changes a measurement from one unit to another without changing the actual quantity. For example, 2 km and 2,000 m are the same distance expressed in different units.

Key Metric Conversions

Length:

• 1 km = 1,000 m
• 1 m = 100 cm
• 1 cm = 10 mm

Mass:

• 1 tonne = 1,000 kg
• 1 kg = 1,000 g

Capacity:

• 1 litre = 1,000 ml
• 1 ml = 1 cm³
• 1 litre = 1,000 cm³

Imperial to Metric Approximations

You need to know these approximate conversions (they are not exact):

• 1 inch ≈ 2.5 cm
• 1 foot ≈ 30 cm
• 1 mile ≈ 1.6 km (or 5 miles ≈ 8 km)
• 1 kg ≈ 2.2 pounds
• 1 gallon ≈ 4.5 litres
• 1 pint ≈ 568 ml

Area and Volume Conversions (Higher)

This is where most errors happen. When converting area, you must square the conversion factor. When converting volume, you must cube it.

• 1 m² = 10,000 cm² (because 100 × 100 = 10,000)
• 1 cm² = 100 mm²
• 1 m³ = 1,000,000 cm³ (because 100 × 100 × 100 = 1,000,000)
• 1 cm³ = 1,000 mm³

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Step-by-Step Method

Simple Metric Conversions

1. Identify the conversion factor between the two units.
2. Decide whether to multiply (going to a smaller unit) or divide (going to a larger unit).
3. Perform the calculation.

Rule of thumb: converting to a smaller unit → the number gets bigger → multiply. Converting to a larger unit → the number gets smaller → divide.

Area and Volume Conversions

1. Find the linear conversion factor (e.g. 1 m = 100 cm).
2. For area, square the factor: 100² = 10,000.
3. For volume, cube the factor: 100³ = 1,000,000.
4. Multiply or divide by the squared or cubed factor as appropriate.

Imperial to Metric

1. Write down the approximate conversion given.
2. Use proportion or multiply/divide as needed.
3. State that the answer is approximate (since imperial-metric conversions at GCSE are approximations).

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Worked Example 1 — Foundation Level

Convert 3.5 km to metres.

Step 1: 1 km = 1,000 m.

Step 2: We are going from a larger unit to a smaller one, so multiply.

Step 3: 3.5 × 1,000 = 3,500 m.

Follow-up: Convert 4,700 g to kg.

Going from smaller to larger, so divide: 4,700 ÷ 1,000 = 4.7 kg.

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Worked Example 2 — Higher Level

Convert 2.5 m² to cm².

Step 1: The linear conversion is 1 m = 100 cm.

Step 2: For area, square the factor: 100² = 10,000.

Step 3: 2.5 × 10,000 = 25,000 cm².

Volume Extension

Convert 0.4 m³ to cm³.

Step 1: Cube the factor: 100³ = 1,000,000.

Step 2: 0.4 × 1,000,000 = 400,000 cm³.

Imperial Conversion

A recipe needs 3 pints of milk. Approximately how many litres is this? (1 pint ≈ 568 ml)

3 × 568 = 1,704 ml = 1,704 ÷ 1,000 = approximately 1.7 litres.

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Common Mistakes

• Forgetting to square or cube for area/volume conversions. Students often use the linear factor (×100) when they should use ×10,000 for area or ×1,000,000 for volume.
• Multiplying when you should divide (or vice versa). Think about whether the answer should be a bigger or smaller number.
• Treating imperial conversions as exact. At GCSE, conversions like 1 mile ≈ 1.6 km are approximate. Use the word "approximately" in your answer.
• Mixing up units of capacity and volume. Remember: 1 ml = 1 cm³ and 1 litre = 1,000 cm³. These are interchangeable.
• Not converting all measurements to the same unit before calculating. If a rectangle has sides given in cm and m, convert both to the same unit before finding area.

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Exam Tips

• Learn the key metric conversions by heart — they are not given on the formula sheet.
• For area and volume conversions, draw a quick diagram showing 1 m = 100 cm, then imagine a 1 m × 1 m square = 100 cm × 100 cm = 10,000 cm².
• Write the conversion factor before you use it. This earns method marks.
• In compound measure questions (density, speed, pressure), you may need to convert units part-way through — e.g. converting g to kg or cm² to m². Watch for this.
• Double-check by estimation. If you convert 3 m² and get 300 cm², that is too small — 3 m² should be 30,000 cm².

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Practice Questions

Question 1 (Foundation) Convert 5,600 mm to metres.

Question 2 (Foundation) A jug holds 2.4 litres. How many millilitres is this?

Question 3 (Higher) Convert 45,000 cm² to m².

Question 4 (Higher) A container has a volume of 0.075 m³. Express this volume in litres. (1 litre = 1,000 cm³)

Question 5 (Foundation) A road is 12 miles long. Approximately how many kilometres is this? (1 mile ≈ 1.6 km)

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Related Topics

• Compound Measures — density, speed and pressure all require consistent units
• Area of 2D Shapes — needed alongside area unit conversions
• Volume of 3D Shapes — needed alongside volume unit conversions
• Scale Drawings and Maps — uses ratio-based unit conversion

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Summary

Unit conversions are essential throughout GCSE Maths. Learn the key metric facts (1 km = 1,000 m, 1 kg = 1,000 g, 1 litre = 1,000 ml = 1,000 cm³) and the approximate imperial equivalents. For area conversions, square the linear factor; for volume conversions, cube it. Always check whether you should multiply or divide by thinking about whether the answer should be bigger or smaller. Careful unit work underpins accurate answers in compound measure questions, so building this skill pays dividends across the entire exam.