Metric and Imperial Conversions –

Unit conversions appear across many GCSE topics, from area and volume calculations to speed and best-buy problems. You need to know the standard metric conversions by heart and the most common imperial approximations.

What Are Metric and Imperial Conversions?

The metric system uses base-10 relationships — each unit is 10, 100, or 1000 times the next. This makes converting between metric units a matter of multiplying or dividing by powers of 10.

Imperial units (inches, feet, miles, pints, pounds) are older measurements still used in everyday life in the UK. You are not expected to memorise every imperial conversion, but you must know the key approximations that let you convert between metric and imperial.

GCSE questions typically give you one conversion fact (e.g., 1 mile ≈ 1.6 km) and ask you to use it to convert between the two systems.

Being confident with metric conversions is also essential for area and volume questions, where the conversion factors are squared or cubed.

Key Formulas

Step-by-Step Method

1. Identify the units you are converting from and to.
2. For metric-to-metric, multiply or divide by the appropriate power of 10.
3. For metric-to-imperial (or vice versa), use the given conversion factor and multiply or divide as needed.

Worked Example 1 — Foundation Level

Question: Convert 3.5 km to metres.

Working: 1 km = 1000 m 3.5 km = 3.5 × 1000 = 3500 m

Answer: 3500 m

Worked Example 2 — Higher Level

Question: A road sign shows a distance of 40 miles. Use 1 mile ≈ 1.6 km to convert this to kilometres.

Working: 40 miles = 40 × 1.6 km = 64 km

Answer: 64 km

Worked Example 3 — Exam Style

Question: A recipe requires 1.5 pints of milk. Use 1 pint ≈ 568 ml. How many litres of milk is this? Give your answer to 2 decimal places.

Working: 1.5 pints = 1.5 × 568 = 852 ml 852 ml ÷ 1000 = 0.852 litres = 0.85 litres (2 d.p.)

Answer: 0.85 litres

Common Mistakes

• Multiplying when you should divide (or vice versa). Converting from a smaller unit to a larger unit means dividing (e.g., mm to cm, divide by 10). Converting from a larger unit to a smaller unit means multiplying.
• Confusing metric and imperial. Do not mix up the two systems in the same calculation. Always convert to the same system before comparing.
• Forgetting area and volume conversions. 1 m² = 10 000 cm² (not 100), and 1 m³ = 1 000 000 cm³ (not 1000). For area, square the conversion factor; for volume, cube it.
• Using inaccurate approximations. Use the approximation given in the question, not a remembered value that might differ.

Exam Tips

• Metric conversions should be memorised — they are rarely given in the question.
• Imperial approximations are usually provided in the question — look for them before starting.
• For area conversions, square the linear factor (e.g., 1 m = 100 cm, so 1 m² = 10 000 cm²).
• For volume conversions, cube the linear factor (e.g., 1 m = 100 cm, so 1 m³ = 1 000 000 cm³).
• A useful check: converting to a smaller unit should give a bigger number; converting to a larger unit should give a smaller number.

Practice Questions

Q1 (Foundation): Convert 4500 g to kilograms.

Q2 (Foundation): Convert 2.8 m to centimetres.

Q3 (Higher): A car travels at 60 mph. Use 1 mile ≈ 1.6 km to find the speed in km/h. Then convert to m/s to 1 decimal place.

Practise metric and imperial conversion questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Unit Conversions
• Speed, Distance and Time
• Compound Measures – Density and Pressure

Summary

• Metric conversions use powers of 10: km → m (×1000), m → cm (×100), cm → mm (×10).
• Mass: 1 kg = 1000 g. Capacity: 1 litre = 1000 ml.
• Key imperial approximations: 1 mile ≈ 1.6 km, 1 inch ≈ 2.5 cm, 1 kg ≈ 2.2 lbs, 1 gallon ≈ 4.5 litres.
• For area conversions, square the linear factor; for volume, cube it.
• Use the conversion factor given in the question for imperial conversions.
• Always check whether you need to multiply or divide — smaller unit to larger unit means divide.