How to Convert Metric Units — KS3 Maths

To convert between metric units, multiply or divide by a power of 10. To go from a larger unit to a smaller unit, multiply. To go from a smaller unit to a larger unit, divide.

The metric prefixes you need to know

The metric system is built on powers of 10. The core prefixes at KS3 are:

Prefix | Symbol | Meaning | Factor
kilo- | k | one thousand | × 1000
(base unit) | — | metres, grams, litres | × 1
centi- | c | one hundredth | ÷ 100
milli- | m | one thousandth | ÷ 1000

The base units you need at KS3 are metres (m) for length, grams (g) for mass, and litres (l) for capacity.

The key conversion facts

Length

Conversion | Factor
1 km = 1000 m | × 1000 to convert km → m
1 m = 100 cm | × 100 to convert m → cm
1 cm = 10 mm | × 10 to convert cm → mm
1 m = 1000 mm | × 1000 to convert m → mm

Mass

Conversion | Factor
1 kg = 1000 g | × 1000 to convert kg → g
1 g = 1000 mg | × 1000 to convert g → mg
1 tonne = 1000 kg | × 1000 to convert tonnes → kg

Capacity

Conversion | Factor
1 litre = 1000 ml | × 1000 to convert l → ml
1 cl = 10 ml | × 10 to convert cl → ml

How to convert metric units — step by step

Step 1 — identify the direction of conversion

Are you going from a larger unit to a smaller unit (e.g. km to m)? You multiply.

Are you going from a smaller unit to a larger unit (e.g. cm to m)? You divide.

Step 2 — identify the conversion factor

Use the table above or recall the key fact (e.g. 1 km = 1000 m, so the factor is 1000).

Step 3 — carry out the calculation

Multiply or divide by the conversion factor.

Step 4 — include the correct unit in your answer

Always write the unit — an answer of "3.5" without units is incomplete.

Worked examples

Example 1 — kilometres to metres

Convert 4.7 km to metres.

km → m: multiply by 1000 (larger to smaller)

4.7 × 1000 = 4700 m

Example 2 — centimetres to metres

Convert 245 cm to metres.

cm → m: divide by 100 (smaller to larger)

245 ÷ 100 = 2.45 m

Example 3 — grams to kilograms

Convert 3600 g to kilograms.

g → kg: divide by 1000 (smaller to larger)

3600 ÷ 1000 = 3.6 kg

Example 4 — millilitres to litres

Convert 850 ml to litres.

ml → l: divide by 1000 (smaller to larger)

850 ÷ 1000 = 0.85 litres

Example 5 — a two-step conversion

Convert 2.3 km to centimetres.

Step 1: 2.3 km to metres → 2.3 × 1000 = 2300 m

Step 2: 2300 m to centimetres → 2300 × 100 = 230 000 cm

Comparing measurements in different units

A common exam question gives two measurements in different units and asks you to compare them. Always convert to the same unit first.

Example: Which is greater — 1.8 m or 195 cm?

Convert 1.8 m to cm: 1.8 × 100 = 180 cm

180 cm < 195 cm, so 195 cm is greater.

Area and volume conversions

Be careful with area and volume — the conversion factor is squared or cubed.

Conversion | Factor
1 m² = 10 000 cm² | (100²)
1 km² = 1 000 000 m² | (1000²)
1 m³ = 1 000 000 cm³ | (100³)
1 litre = 1000 cm³ | useful link between capacity and volume

Example: Convert 5 m² to cm².

5 × 10 000 = 50 000 cm²

Metric units in the national curriculum

The DfE's KS3 mathematics programme of study requires pupils to use standard units of measurement for length, mass, and capacity, including decimal quantities, and to convert between standard metric units. BBC Bitesize's KS3 measurement section confirms that metric conversions appear in both non-calculator and calculator exam papers throughout Year 7 to Year 9.

Frequently asked questions

How do I remember whether to multiply or divide when converting metric units?

Think about the size of the units. A kilometre is bigger than a metre, so 1 km equals many metres — you must multiply to get the bigger number. Conversely, centimetres are smaller than metres, so converting cm to m gives a smaller number — you divide. A useful phrase: "going smaller → bigger number → multiply."

Why do metric conversions always involve 10, 100, or 1000?

The metric system was designed on powers of 10 so that conversions are always a matter of moving the decimal point. Each prefix represents a factor of 10 relative to the next. This makes metric calculations much simpler than imperial conversions (e.g. 1 mile = 1760 yards), and is why the metric system is used in science and medicine worldwide.

What is the difference between mass and weight at KS3?

In everyday KS3 maths, "weight" and "mass" are often used interchangeably, and both are measured in kilograms or grams. Strictly speaking, mass is the amount of matter in an object (measured in kg), while weight is a force measured in newtons. KS3 maths questions use kilograms and grams and treat them as weight — the physics distinction is introduced more formally in science lessons.

How do I convert square metres to square centimetres?

Because area is two-dimensional, the conversion factor is squared. Since 1 m = 100 cm, 1 m² = 100 × 100 = 10 000 cm². So multiply by 10 000, not 100. For example, 4 m² = 4 × 10 000 = 40 000 cm². This catches many pupils out who use 100 instead of 10 000.

For personalised KS3 maths tutoring on measures and conversions — visit aitutors.me.