Units and Conversions

This lesson covers DfE content statements L2.14 and L2.15 — converting between metric units, converting between metric and imperial units using conversion factors, and calculating with compound measures (speed, density, rates of pay).

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Metric Units

The metric system is based on powers of 10, making conversions straightforward.

Length

Unit	Abbreviation	Relationship
Millimetre	mm	10 mm = 1 cm
Centimetre	cm	100 cm = 1 m
Metre	m	1,000 m = 1 km
Kilometre	km	Base unit for long distances

Mass (Weight)

Unit	Abbreviation	Relationship
Milligram	mg	1,000 mg = 1 g
Gram	g	1,000 g = 1 kg
Kilogram	kg	1,000 kg = 1 tonne
Tonne	t	—

Capacity (Volume)

Unit	Abbreviation	Relationship
Millilitre	ml	1,000 ml = 1 litre
Centilitre	cl	100 cl = 1 litre
Litre	l	—

Key fact: 1 ml = 1 cm³ (one cubic centimetre).

Worked Example — Converting Metric Units

Scenario: A recipe requires 1.75 kg of flour. You have a 500g bag and a 1 kg bag. Is that enough?

500g + 1,000g = 1,500g. You need 1,750g (1.75 × 1,000). So no, you are 250g short.

Worked Example — Building Materials

Scenario: A builder needs 3.5 m of timber. The timber yard sells lengths in centimetres. How many centimetres is this?

3.5 × 100 = 350 cm

Exam Tip: When converting metric units, remember: multiply when going to a smaller unit, divide when going to a larger unit. A useful mnemonic: "going smaller → number gets bigger."

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Imperial Units

Although the UK mostly uses metric, imperial units are still common in everyday life.

Length

Unit	Abbreviation	Relationship
Inch	in	12 inches = 1 foot
Foot	ft	3 feet = 1 yard
Yard	yd	1,760 yards = 1 mile
Mile	mi	—

Mass

Unit	Abbreviation	Relationship
Ounce	oz	16 ounces = 1 pound
Pound	lb	14 pounds = 1 stone
Stone	st	—

Capacity

Unit	Abbreviation	Relationship
Pint	pt	8 pints = 1 gallon
Gallon	gal	—

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Metric-Imperial Conversions

You are expected to know (or use given) approximate conversion factors.

Metric	≈ Imperial	Conversion factor
1 km	0.625 miles	5 miles ≈ 8 km
1 m	3.3 feet	1 foot ≈ 30 cm
2.54 cm	1 inch	1 inch = 2.54 cm
1 kg	2.2 pounds	1 lb ≈ 454g
1 litre	1.75 pints	1 pint ≈ 568 ml
4.5 litres	1 gallon	1 gallon ≈ 4.5 litres

Worked Example — Driving Abroad

Scenario: A road sign in France says the next town is 120 km away. Roughly how many miles is that?

Using 8 km ≈ 5 miles: 120 ÷ 8 = 15 groups → 15 × 5 = 75 miles

Worked Example — Cooking from an American Recipe

Scenario: An American recipe calls for 2 pounds of chicken. How many grams is that?

1 lb ≈ 454g → 2 lb = 2 × 454 = 908g (approximately 900g)

Worked Example — Height

Scenario: A person is 5 feet 8 inches tall. What is their height in centimetres?

5 feet 8 inches = (5 × 12) + 8 = 68 inches 68 × 2.54 = 172.72 cm ≈ 173 cm

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Conversion Graphs

Conversion graphs provide a visual way to convert between units. Read across from one axis and down (or up) to the other.

graph LR
    A[Read value on<br/>one axis] --> B[Draw horizontal/<br/>vertical line to<br/>the graph line]
    B --> C[Draw vertical/<br/>horizontal line<br/>to other axis]
    C --> D[Read the<br/>converted value]

Worked Example

Scenario: A conversion graph shows that 10 miles ≈ 16 km. Use this to estimate 35 miles in km.

From the graph (which is a straight line through the origin): 35 miles → 56 km

Check: 35 × 1.6 = 56 ✓

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Compound Measures

Compound measures combine two different units.

Speed

Speed = Distance ÷ Time