Units of Measure
Understanding units of measurement is essential for solving problems in real-world contexts. This guide covers units of length, area, volume, speed, density, pressure, unit pricing, and how to convert between different units effectively.
Units of Length
Common Units of Length
| Unit | Abbreviation | Equivalent |
|---|---|---|
| Millimetre | mm | 1 mm = 0.001 m |
| Centimetre | cm | 1 cm = 10 mm = 0.01 m |
| Metre | m | 1 m = 100 cm = 1000 mm |
| Kilometre | km | 1 km = 1000 m |
Imperial to Metric Conversions
| Imperial Unit | Equivalent Metric Value |
|---|---|
| 1 inch (in) | 2.54 cm |
| 1 foot (ft) | 30.48 cm |
| 1 yard (yd) | 0.914 m |
| 1 mile (mi) | 1.609 km |
Units of Area and Volume
Units of Area
| Unit | Abbreviation | Equivalent |
|---|---|---|
| Square millimetre | mm² | $1 mm² = 10^{-6} m²$ |
| Square centimetre | cm² | $1 cm² = 10^{-4} m²$ |
| Square metre | m² | $1 m² = 10,000 cm²$ |
| Square kilometre | km² | $1 km² = 1,000,000 m²$ |
| Hectare | ha | $1 ha = 10,000 m²$ |
Units of Volume
| Unit | Abbreviation | Equivalent |
|---|---|---|
| Cubic millimetre | mm³ | $1 mm³ = 10^{-9} m³$ |
| Cubic centimetre | cm³ | $1 cm³ = 10^{-6} m³$ |
| Cubic metre | m³ | $1 m³ = 1,000,000 cm³$ |
| Litre | L | $1 L = 1000 cm³ = 0.001 m³$ |
| Millilitre | mL | $1 mL = 1 cm³$ |
Imperial to Metric Conversions
| Imperial Unit | Equivalent Metric Value |
|---|---|
| 1 square inch (in²) | 6.45 cm² |
| 1 square foot (ft²) | 0.093 m² |
| 1 square yard (yd²) | 0.836 m² |
| 1 cubic inch (in³) | 16.39 cm³ |
| 1 cubic foot (ft³) | 0.0283 m³ |
| 1 gallon (UK) | 4.546 L |
Speed, Density, and Pressure
Speed
Speed is the rate of distance covered per unit of time:
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
| Unit | Equivalent |
|---|---|
| Metres per second | m/s |
| Kilometres per hour | km/h |
| Miles per hour | mph |
Conversions:
- 111 m/s = 3.63.63.6 km/h
- 111 mph ≈ 1.6091.6091.609 km/h
Density
Density is mass per unit volume:
$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$
| Unit | Equivalent |
|---|---|
| Grams per cubic centimetre | g/cm³ |
| Kilograms per cubic metre | kg/m³ |
Conversion:
- 111 g/cm³ = 100010001000 kg/m³
Pressure
Pressure is force per unit area:
$$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$$
| Unit | Equivalent |
|---|---|
| Pascals | 1 Pa = 1 N/m² |
| Newtons per square centimetre | 1 N/cm² = 10,000 N/m² |
Conversions:
- 111 atmosphere (atm) ≈ 101,325101,325101,325 Pa
- 111 bar = 100,000100,000100,000 Pa
Unit Pricing
Unit pricing is used to compare prices of items sold in different quantities.
$$\text{Unit Price} = \frac{\text{Total Cost}}{\text{Quantity}}$$
For example, if 500 g of cheese costs £4, the unit price per gram is:
$$\frac{4}{500} = 0.008 \text{ (£ per gram)}$$
To compare different-sized packs, convert costs to a common unit (e.g., per 100 g or per kg).
Changing Between Units of Measurement
Length Conversion
Multiply or divide by powers of 10 when converting between metric units.
For example:
$$1.2 \text{ km} = 1200 \text{ m}$$
$$150 \text{ cm} = 1.5 \text{ m}$$
Converting Units of Area
To convert between metric units of area:
- Multiply/divide by $100^2 = 10,000$ when moving between m² and cm².
- Multiply/divide by $1000^2 = 1,000,000$ when moving between km² and m².
Example:
$$2 \text{ m²} = 20,000 \text{ cm²}$$
Converting Units of Volume
To convert between metric units of volume:
- Multiply/divide by $100^3 = 1,000,000$ when moving between m³ and cm³.
- 1 m³ = 1000 L, so multiply/divide by 1000 when converting between m³ and litres.
Example:
$$3.5 \text{ m³} = 3,500 \text{ L}$$
Converting Speed, Density, and Pressure
Speed
To convert km/h to m/s:
$$\text{Speed in m/s} = \frac{\text{Speed in km/h}}{3.6}$$
Example:
$$72 \text{ km/h} = \frac{72}{3.6} = 20 \text{ m/s}$$
Density
To convert g/cm³ to kg/m³:
$$\text{Density in kg/m³} = \text{Density in g/cm³} \times 1000$$
Example:
$$2.5 \text{ g/cm³} = 2500 \text{ kg/m³}$$
Pressure
To convert N/cm² to Pa:
$$\text{Pressure in Pa} = \text{Pressure in N/cm²} \times 10,000$$
Example:
$$3 \text{ N/cm²} = 30,000 \text{ Pa}$$
Exam Tips
✔ Memorise key conversions—especially for metric-imperial conversions.
✔ Show full working when converting between units.
✔ Check whether to multiply or divide when converting.
✔ Be consistent with units in calculations to avoid errors.
✔ Use common sense—if an answer seems too large or small, check your conversion.
This guide provides the essential knowledge for tackling units of measurement in GCSE Maths. Practise plenty of conversion problems to build confidence.
