Home / IGCSE Maths 0580 / Mensuration / Units of measure and conversions
Cambridge IGCSE · Topic 5.1
IGCSE Maths 0580 / Topic 5 / IGCSE

Same amount, new units.

Metres, litres and kilograms are easy to swap once you know the multipliers. The catch is area and volume: square and cubic units do not convert by 10, 100 or 1000 the way lengths do.

Full-screen labArea and perimeter lab → Topic 5All mensuration lessons →
The key idea

Convert a length first, then square it for area or cube it for volume. Since \(1\text{ m} = 100\text{ cm}\), \(1\text{ m}^2 = 100^2 = 10\,000\text{ cm}^2\) and \(1\text{ m}^3 = 100^3 = 1\,000\,000\text{ cm}^3\). For capacity, \(1\text{ cm}^3 = 1\text{ ml}\) and \(1000\text{ cm}^3 = 1\) litre.

1 cm = 10 mm 1 cm² = 10 × 10 = 100 mm² each small square is 1 mm²
Fig. 1: a 1 cm square is 10 mm by 10 mm, so it holds 100 squares of 1 mm2, not 10
Section 01

Length, mass and capacity.

In the lab, pick a quantity, type a value and switch between units. Notice which way the number moves: changing to a SMALLER unit needs MORE of them, so you multiply; changing to a bigger unit, you divide.

QuantityFacts to learn
Length10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km
Mass1000 g = 1 kg
Capacity1000 ml = 1 l
Worked example Big unit to small unit
Convert (a) 3.75 km to metres (b) 0.6 litres to millilitres.
  1. (a) Metres are smaller than kilometres, so there are more of them: multiply by 1000.
  2. \(3.75 \times 1000 = 3750\).
  3. (b) Millilitres are smaller, so multiply by 1000: \(0.6 \times 1000 = 600\).
Answer: (a) 3750 m   (b) 600 ml
Worked example Small unit to big unit
Convert (a) 2450 g to kilograms (b) 86 mm to centimetres.
  1. (a) Kilograms are bigger, so there are fewer of them: divide by 1000.
  2. \(2450 \div 1000 = 2.45\).
  3. (b) 10 mm make 1 cm, so divide by 10: \(86 \div 10 = 8.6\).
Answer: (a) 2.45 kg   (b) 8.6 cm
Examiner trap

Check the answer makes sense: 3.75 km is a long walk, so the number of metres must be LARGE (3750), not 0.003 75. If the number got smaller when you moved to a smaller unit, you divided when you should have multiplied.

Section 02

Area units are squared.

A square of side 1 cm is 10 mm by 10 mm (Fig. 1), so it contains \(10 \times 10 = 100\) squares of 1 mm2. Square the length factor every time.

LengthArea
1 cm = 10 mm1 cm2 = 100 mm2
1 m = 100 cm1 m2 = 10 000 cm2
1 km = 1000 m1 km2 = 1 000 000 m2
Worked example m² to cm²
Convert \(3.2\text{ m}^2\) to \(\text{cm}^2\).
  1. \(1\text{ m} = 100\text{ cm}\), so \(1\text{ m}^2 = 100 \times 100 = 10\,000\text{ cm}^2\).
  2. Smaller unit, so multiply: \(3.2 \times 10\,000 = 32\,000\).
Answer: \(32\,000\text{ cm}^2\)
Worked example mm² to cm²
Convert \(45\,000\text{ mm}^2\) to \(\text{cm}^2\).
  1. \(1\text{ cm}^2 = 10 \times 10 = 100\text{ mm}^2\).
  2. Bigger unit, so divide: \(45\,000 \div 100 = 450\).
Answer: \(450\text{ cm}^2\)
Worked example Mixed units in a rectangle
A table top measures 2.4 m by 85 cm. Find its area in (a) \(\text{cm}^2\) (b) \(\text{m}^2\).
  1. Put both lengths in the same unit first: \(2.4\text{ m} = 240\text{ cm}\).
  2. (a) Area \(= 240 \times 85 = 20\,400\text{ cm}^2\).
  3. (b) Divide by \(10\,000\): \(20\,400 \div 10\,000 = 2.04\). (Check: \(2.4 \times 0.85 = 2.04\).)
Answer: (a) \(20\,400\text{ cm}^2\)   (b) \(2.04\text{ m}^2\)
Your turn
Convert \(7500\text{ cm}^2\) to \(\text{m}^2\).
Examiner trap

\(1\text{ m}^2\) is NOT \(100\text{ cm}^2\). A square metre is 100 cm by 100 cm, which is \(10\,000\text{ cm}^2\). Using 100 is the most common lost mark in this topic.

Stage 1 · Learn

Check your understanding

Four quick checks. Each correct answer earns XP and records this skill on your profile.

Quick check+10 XP

Convert 5.2 km to metres.

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How many \(\text{cm}^2\) are in \(1\text{ m}^2\)?

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How many \(\text{mm}^3\) are in \(1\text{ cm}^3\)?

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A bottle holds \(750\text{ cm}^3\). What is this in litres?

Section 03

Volume and capacity.

Volume units are cubed: cube the length factor. Then link volume to capacity with \(1\text{ cm}^3 = 1\text{ ml}\).

Worked example m³ to cm³
Convert \(0.35\text{ m}^3\) to \(\text{cm}^3\).
  1. \(1\text{ m}^3 = 1\,000\,000\text{ cm}^3\).
  2. \(0.35 \times 1\,000\,000 = 350\,000\).
Answer: \(350\,000\text{ cm}^3\)
Worked example A tank in litres
A tank is a cuboid 2 m long, 1.5 m wide and 0.8 m high. How many litres does it hold when full?
  1. Volume \(= 2 \times 1.5 \times 0.8 = 2.4\text{ m}^3\).
  2. \(1\text{ m}^3 = 1000\) litres, so \(2.4 \times 1000 = 2400\) litres.
Answer: 2400 litres
Your turn
Convert \(4500\text{ mm}^3\) to \(\text{cm}^3\).
Examiner trap

\(1\text{ m}^3\) is 1000 litres, not 100 and not 1 million. Go through cm3 if unsure: \(1\,000\,000\text{ cm}^3 \div 1000 = 1000\) litres.

Section 04

Units in problems.

Exam questions mix units on purpose. Change everything to one unit before you calculate, and give the answer in the unit the question asks for.

Worked example How many glasses?
A jug holds 3.5 litres of juice. How many 250 ml glasses can be filled from it?
  1. Same unit: \(3.5\text{ l} = 3500\text{ ml}\).
  2. \(3500 \div 250 = 14\).
Answer: 14 glasses
Worked example Portions by mass
A bag holds 1.2 kg of rice. Each portion is 150 g. How many portions are in the bag?
  1. Same unit: \(1.2\text{ kg} = 1200\text{ g}\).
  2. \(1200 \div 150 = 8\).
Answer: 8 portions
Examiner trap

When the answer must be a whole number of objects (glasses, bottles, tiles), decide whether to round down (how many can be FILLED) or up (how many are NEEDED). Do not just round to the nearest.

Stage 2 · Exam

Exam-style questions

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A fish tank is a cuboid 60 cm by 40 cm by 30 cm. How many litres of water does it hold when full?

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Convert \(0.045\text{ m}^2\) to \(\text{cm}^2\).

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A nature reserve has an area of \(3.6\text{ km}^2\). What is this in \(\text{m}^2\)?

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A tank measures 1.5 m by 0.8 m by 0.5 m. Water flows in at 12 litres per minute. How long does it take to fill the empty tank?

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Go deeper · practice
Six original Cambridge-style questions
Length, mass and capacity conversions, area and volume units, a carpet cost and a water tank emptied into bottles.