Converting between standard and compound units
Unit conversion is one of the most common low-mark tasks in GCSE Maths and slips into almost every applied topic — speed, density, ratio problems, and even algebra. The skill divides into two layers: simple unit conversions (within length, mass, time, money, area, volume) and compound unit conversions (combinations such as m/s ↔ km/h or g/cm³ ↔ kg/m³).
Simple conversions — keep a conversion table in your head
| Quantity | Conversion |
|---|---|
| Length | 10 mm = 1 cm; 100 cm = 1 m; 1000 m = 1 km |
| Mass | 1000 mg = 1 g; 1000 g = 1 kg; 1000 kg = 1 tonne |
| Capacity | 1000 ml = 1 litre; 1 cm³ = 1 ml |
| Time | 60 s = 1 min; 60 min = 1 h; 24 h = 1 day |
Worked example: convert 3.4 km to cm. 3.4 km × 1000 = 3400 m × 100 = 340 000 cm.
Area and volume — square or cube the linear factor
If 1 m = 100 cm, then 1 m² = 100 × 100 = 10 000 cm², and 1 m³ = 100 × 100 × 100 = 1 000 000 cm³. Always square or cube the conversion factor for area or volume.
Worked example: convert 2.5 m² to cm². 2.5 × 10 000 = 25 000 cm².
Compound units — convert each part separately
A compound unit is a ratio of two units, e.g. m/s (length per time) or g/cm³ (mass per volume). To convert, change the numerator and denominator independently.
Worked example: convert 72 km/h to m/s.
- 72 km = 72 000 m, 1 h = 3600 s.
- 72 km/h = 72 000 ÷ 3600 = 20 m/s.
Quick fact to memorise: × by 5/18 to go km/h → m/s, × by 18/5 to go m/s → km/h.
Worked example: convert 8.5 g/cm³ to kg/m³.
- 1 g = 0.001 kg, so 8.5 g = 0.0085 kg.
- 1 cm³ = 0.000001 m³, so 1/cm³ = 1 000 000 /m³.
- 8.5 g/cm³ = 0.0085 × 1 000 000 = 8500 kg/m³.
Memorise: g/cm³ × 1000 = kg/m³.
Money
£1 = 100 p. Be careful when comparing prices in pence and pounds in the same problem — convert to a common unit first.
⚠Common mistakes— Common mistakes (examiner traps)
- Forgetting to square or cube for area/volume conversions (treating 1 m² = 100 cm²).
- Multiplying when you should divide — sketch the units to check the result has the right size.
- Mixing units mid-calculation — convert everything before doing arithmetic.
- Compound unit slip — changing numerator only and forgetting the denominator.
- Time conversions — 1.5 hours is 90 min, not 150 min; 2 h 15 min = 2.25 h, not 2.15 h.
➜Try this— Quick check
A car travels at 25 m/s. How fast is this in km/h? Answer: 25 × 18/5 = 90 km/h.
AI-generated · claude-opus-4-7 · v3-deep-ratio