GCSE maths requires you to convert between metric and imperial units using approximate equivalents — some given in the exam, some memorised. The key facts are 1 inch ≈ 2.54 cm, 1 mile ≈ 1.6 km, and 1 kg ≈ 2.2 lb. Knowing these and the direction of conversion covers most exam questions.
Which conversions must I know for GCSE?
The AQA GCSE specification expects candidates to use approximate conversion factors. The most frequently tested are:
| Quantity | Imperial unit | Metric equivalent |
|---|---|---|
| Length | 1 inch | ≈ 2.54 cm |
| Length | 1 foot (= 12 inches) | ≈ 30 cm |
| Length | 1 mile | ≈ 1.6 km (or 8 km ≈ 5 miles) |
| Length | 1 yard (≈ 3 feet) | ≈ 0.91 m |
| Mass | 1 pound (lb) | ≈ 454 g |
| Mass | 1 stone (= 14 lb) | ≈ 6.35 kg |
| Mass | 1 kg | ≈ 2.2 lb |
| Capacity | 1 pint | ≈ 568 ml (≈ 0.57 litres) |
| Capacity | 1 gallon (= 8 pints) | ≈ 4.55 litres |
Many questions provide the conversion factor within them — read the question carefully before deciding what to memorise. The "8 km ≈ 5 miles" form of the miles–km conversion is often more useful for mental calculation than 1 mile ≈ 1.6 km.
How do you convert from imperial to metric?
Rule: multiply by the metric equivalent per imperial unit.
Example: convert 6 miles to kilometres.
- 1 mile ≈ 1.6 km
- 6 miles ≈ 6 × 1.6 = 9.6 km
Example: convert 5 inches to centimetres.
- 1 inch ≈ 2.54 cm
- 5 inches ≈ 5 × 2.54 = 12.7 cm
Think: you are moving from imperial (large-sounding units) to metric (smaller-sounding in length), so you expect more centimetres than inches. 5 inches giving 12.7 cm makes sense.
How do you convert from metric to imperial?
Rule: divide by the metric equivalent per imperial unit (or multiply by the reciprocal).
Example: convert 10 km to miles.
- 1 mile ≈ 1.6 km, so 1 km ≈ 1/1.6 miles
- 10 km ≈ 10 ÷ 1.6 = 6.25 miles
Alternatively, use the ratio form 8 km : 5 miles:
- 10 km × (5 miles / 8 km) = 10 × 5/8 = 50/8 = 6.25 miles ✓
Example: convert 3.3 kg to pounds.
- 1 kg ≈ 2.2 lb
- 3.3 kg ≈ 3.3 × 2.2 = 7.26 lb
How do compound unit conversions work?
A compound unit involves two base units, such as speed (distance per time) or pressure (force per area). To convert, change each base unit separately.
Example: convert 60 miles per hour to kilometres per hour.
- 60 miles × 1.6 km/mile = 96 km/h
Example: convert 80 km/h to miles per hour.
- 80 km ÷ 1.6 = 50 mph
(The 80 km/h national speed-limit equivalent is exactly 50 mph, which is a useful memory anchor.)
Exam tips for conversion questions
- Identify the conversion factor from the question or your memorised list before calculating.
- Check the direction: metric to imperial divides; imperial to metric multiplies (for length and mass). Use an estimate to check the direction makes sense.
- Use the ratio method for non-standard problems — set up a proportion: 8 km = 5 miles, so ? km = 12 miles → ? = 12 × 8/5 = 19.2 km.
- Show your working. A numerical error on a two-mark question still earns the method mark if the conversion factor and approach are clear.
- Quote units clearly in the answer. "9.6" without km is incomplete.
Frequently asked questions
Are metric–imperial conversions given in the exam?
Some are, some are not — it depends on the exam board and paper tier. AQA typically provides the conversion factor in the question if it expects you to use a less common one (e.g. litres to gallons). However, miles to km and kg to lb are commonly expected from memory. Learn both the metric-to-imperial direction (kg → lb: multiply by 2.2) and imperial-to-metric direction (lb → kg: divide by 2.2).
What is the difference between a pound (mass) and a pint (volume)?
A pound (lb) measures mass. A pint measures liquid volume (capacity). They are entirely different quantities, but both are imperial units — students occasionally mix them. Mass: 1 kg ≈ 2.2 lb. Capacity: 1 pint ≈ 568 ml.
How do I remember whether to multiply or divide?
Ask: "am I getting more units or fewer?" Inches to cm: centimetres are smaller, so there will be more of them — multiply. Km to miles: miles are longer, so there will be fewer of them — divide. If the answer seems unreasonably large or small, you have probably gone in the wrong direction.
Can I convert miles and kilometres using the 8 : 5 ratio?
Yes — this is often quicker than using 1.6. Write the ratio: 8 km = 5 miles. Then multiply both sides by whatever scale factor puts the given quantity on one side. For 24 km: 24 ÷ 8 = 3, so multiply both sides by 3: 24 km = 15 miles.
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