Standard units in geometry

WJEC examines unit fluency on every paper. Most errors come from area/volume conversions and from confusing capacity with volume.

Length conversions

• 10 mm = 1 cm
• 100 cm = 1 m
• 1000 m = 1 km

So 1 m = 1000 mm; 1 km = 100 000 cm = 1 000 000 mm.

Area conversions

Areas use the SQUARE of the linear factor:

• 1 cm² = 100 mm² (since 1 cm = 10 mm; squared gives 100).
• 1 m² = 10 000 cm².
• 1 km² = 1 000 000 m².

Volume conversions

Volumes use the CUBE of the linear factor:

• 1 cm³ = 1000 mm³.
• 1 m³ = 1 000 000 cm³.

Capacity (volume of liquid)

• 1 litre = 1000 ml.
• 1 ml = 1 cm³ exactly.
• 1 litre = 1000 cm³.
• 1 m³ = 1000 litres.

Mass

• 1 g = 1000 mg.
• 1 kg = 1000 g.
• 1 tonne = 1000 kg.

Time

• 60 s = 1 min; 60 min = 1 h; 24 h = 1 day; 7 days = 1 week.
• Decimal-time trap: 1 h 45 min = 1.75 h, NOT 1.45 h.

Money

UK money: £1 = 100p. Always settle on a single unit (£ OR p) before adding.

Currency conversion uses an exchange rate: pounds × rate = foreign currency; foreign / rate = pounds.

Quick reference table

Quantity	Smaller	Larger	Factor
Length	mm	cm	× 10
Length	cm	m	× 100
Length	m	km	× 1000
Area	cm²	m²	× 10 000
Volume	cm³	m³	× 1 000 000
Capacity	ml	l	× 1000
Mass	g	kg	× 1000

WJEC exam tip

If a question gives mixed units (e.g. height in cm, width in m), CONVERT FIRST before any calculation. This is worth 1 method mark on every WJEC mensuration question.