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Imperial conversions
Inches to centimetres, pounds to kilograms, pints to litres and miles to kilometres.
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Long ago, Britain measured everything in imperial units: inches, miles, pounds and pints. Today we use metric units for most things, but the old ones have not gone away. Road signs show miles, milk can come in pints, and lots of rulers have inches along one edge. In this lesson you will learn how to:
- say what inches, miles, pounds and pints measure, and roughly how big they are
- change inches into centimetres and back
- change kilograms into pounds and back
- change pints into litres and back
- change miles into kilometres and back
- solve problems that mix imperial and metric units
Dark blue: whole numbers
Red dot: the decimal point
Blue: digits after the point
1. Imperial units: how big is each one?
Key idea
Imperial units do not fit neatly with metric units, so we change between them with rough rates:
numbers that are close enough and easy to work with. The sign ≈ means “is about”,
so 1 inch ≈ 2.5 cm says “1 inch is about 2.5 cm”.
| Imperial unit | It measures | It is about |
|---|---|---|
| inch (in) | length | 2.5 cm, about the width of a grown-up’s thumb |
| mile | long distances | 1.6 km, so 5 miles is about 8 km |
| pound (lb) | mass | 450 g, a bit less than half a kilogram |
| pint (pt) | capacity | 570 ml, a bit more than half a litre |
The rates to learn
1 inch ≈ 2.5 cm1 kg ≈ 2.2 lb1 lb ≈ 450 g1 pint ≈ 570 ml1 litre ≈ 1.75 pints5 miles ≈ 8 km
The exact numbers are messier: 1 inch is exactly 2.54 cm, and 1 mile is about 1.609 km. That is why we use the rough rates. If a question gives you a rate, use the one it gives.
Watch out
A pound (lb) here is a mass, like a kilogram. It is not the same as a pound (£) of money, even
though they share a name. “lb” comes from libra, the Roman word for a pound.
Which is bigger?
How to play
- Tap the amount you think is bigger. Then watch the bars grow to their real sizes.
- Two in a row with no slips moves you up a level. Level 1 has one of each unit, level 2 has more than one, and on level 3 they are closer together.
2. Inches and centimetres
Key idea
1 inch ≈ 2.5 cm. An inch is longer than a centimetre, so there are more centimetres
than inches. Inches to centimetres: multiply by 2.5. Centimetres to inches: divide by 2.5.
Example 1: the pencil is 6 inches long. About how many centimetres is that?
- Inches to centimetres: multiply by 2.5. An easy way: double it, then add half of it:6 × 2 = 12, half of 6 = 3
- Add them:12 + 3 = 15
Answer6 inches ≈ 15 cm. The ruler shows it is just past 15 cm.
Example 2: about how many inches is 20 cm?
- Centimetres to inches: divide by 2.5. An easy way: divide by 5, then double:20 ÷ 5 = 4
- Double it:4 × 2 = 8
Answer20 cm ≈ 8 inches.
Watch out
Check your answer makes sense. Centimetres are small, so the number of centimetres is always bigger
than the number of inches. 20 cm is 8 inches, not 50 inches.
The two-edged ruler
How to play
- Drag the red point of the pencil (or use the arrow keys) to make it the length asked for, and press Check. Then use the rate to change it into the other unit.
- Two with no slips moves you up a level. Level 1 goes from inches to centimetres, level 2 from centimetres to inches, and level 3 mixes both with harder numbers.
3. Pounds and kilograms
Key idea
1 kg ≈ 2.2 lb. A kilogram is heavier than a pound: a pound is a bit less than half a
kilogram, about 450 g. Kilograms to pounds: multiply by 2.2. The easy way: double it, then add a
tenth of the double.
Some kitchen scales show both
The needle is on 2 kg. On the inside ring it is between 4 and 5 lb, a little less than halfway: 2 kg ≈ 4.4 lb.
Example 1: about how many pounds is 5 kg?
- Double it:5 × 2 = 10
- A tenth of the double:10 ÷ 10 = 1
- Add them:10 + 1 = 11
Answer5 kg ≈ 11 lb
Example 2: about how many kilograms is 11 lb?
- Each kilogram is about 2.2 lb. Count up in 2.2s:2.2, 4.4, 6.6, 8.8, 11
- That is 5 lots of 2.2:11 ÷ 2.2 = 5
Answer11 lb ≈ 5 kg
Watch out
× 2.2 is a bit more than doubling, so do not stop at the double. 5 kg is about 11 lb, not 10 lb.
And the number of pounds is always bigger than the number of kilograms.
Double it and add a bit
How it works
- Follow the steps and type each number. The . key is the decimal point. When you finish, the scale shows the real amount.
- Two with no slips moves you up a level. Level 1 is whole kilograms to pounds, level 2 is pounds to kilograms, and level 3 has halves.
4. Pints and litres
Key idea
1 pint ≈ 570 ml: a bit more than half a litre. Going the other way, 1 litre ≈ 1.75
pints, so 4 litres ≈ 7 pints. A pint is smaller than a litre, so there are more pints than
litres.
A jug with two scales
The water is at 2 pints. On the millilitre side it is a little more than 1100 ml, so 2 pints is a bit more than 1 litre.
Example 1: about how many millilitres is 2 pints?
- Each pint is about 570 ml:2 × 570 = 1140
Answer2 pints ≈ 1140 ml, just over 1 litre.
Example 2: about how many pints is 8 litres?
- 4 litres ≈ 7 pints. How many 4s make 8?8 ÷ 4 = 2
- So it is 2 lots of 7 pints:2 × 7 = 14
Answer8 litres ≈ 14 pints
Watch out
A pint is smaller than a litre. 2 pints is only a little more than 1 litre, and 3 pints is less than
2 litres.
The two-scale jug
How to play
- Drag the water up or down (or use the arrow keys) to the amount asked for, and press Check. Then answer the question about the other side of the jug.
- Two with no slips moves you up a level. Level 1 compares pints with litres, level 2 starts from millilitres, and level 3 uses 1 pint ≈ 570 ml.
5. Miles and kilometres
Key idea
5 miles ≈ 8 km. A mile is longer than a kilometre (1 mile ≈ 1.6 km). Think of a road
with a post every 5 miles: every post is another 8 km. Count the jumps.
The road
Example 1: about how many kilometres is 15 miles?
- How many jumps of 5 miles?15 ÷ 5 = 3
- Each jump is 8 km:3 × 8 = 24
Answer15 miles ≈ 24 km
Example 2: about how many miles is 40 km?
- How many jumps of 8 km?40 ÷ 8 = 5
- Each jump is 5 miles:5 × 5 = 25
Answer40 km ≈ 25 miles
Watch out
The rate is 5 miles to 8 km, not 1 mile to 8 km. A mile is only a little longer than a kilometre,
so the two numbers should be fairly close: 40 km is 25 miles, not 320.
The long road
How to play
- Tap the post where the distance is, then type the distance in the other unit.
- Two with no slips moves you up a level. Level 1 goes from miles to kilometres, level 2 from kilometres to miles, and on level 3 the journey is too long for the road, so you work it out.
6. Problems with imperial and metric units
Key idea
To compare two amounts, or to add or take them away, first put them into the same unit. Then
answer the question. Use the rate the question gives you.
Example 1: Mia cycles 10 miles. Leo cycles 15 km. Who goes further, and by about how much?
- Change the miles into km. 10 miles is 2 jumps of 5 miles:2 × 8 = 16 km
- Compare:16 − 15 = 1
AnswerMia goes further, by about 1 km.
Example 2: a cake needs 2 lb of flour. Is a 1 kg bag enough?
- Change the kilograms into pounds:1 kg ≈ 2.2 lb
- Compare:2.2 lb is more than 2 lb
AnswerYes, with about 0.2 lb to spare.
Watch out
Use the rate in the question, even if it is not the one you learned. If it says “1 mile is about
1.6 km”, then 10 miles is 10 × 1.6 = 16 km.
Conversion workshop
How it works
- Follow the steps and type each number. The . key is the decimal point.
- Two with no slips moves you up a level. Level 1 is inches and miles, level 2 is pounds and pints, level 3 goes back the other way, level 4 compares two amounts, and level 5 has two-step stories.
7. Practice: pick your level
Start with Foundation if you are in Year 4 or just starting. Move up when you are getting most of them right.
The mistakes that cost marks
- Going the wrong way. Multiplying 20 cm by 2.5 to get 50 inches. an inch is bigger than a centimetre, so there are fewer inches: divide. 20 cm ≈ 8 inches.
- Thinking a pound is heavier than a kilogram. 1 kg ≈ 2.2 lb, so a kilogram is more than twice as heavy as a pound.
- Thinking a pint is bigger than a litre. a pint is about 570 ml, a bit more than half a litre.
- Using 1 mile ≈ 8 km. the rate is 5 miles ≈ 8 km, or 1 mile ≈ 1.6 km.
- Stopping at the double. Saying 5 kg is 10 lb. × 2.2 is the double plus a tenth of the double: 10 + 1 = 11 lb.
- Ignoring the rate in the question. Using 2.5 when the question says 1 inch = 2.54 cm. always use the rate the question gives you.
- Comparing without converting. Saying 10 miles is less than 15 km because 10 is less than 15. put both into the same unit first: 10 miles ≈ 16 km, which is more.
- Mixing up pounds. Treating a pound (lb) of flour as money. lb is a mass. £ is money.
Quick checklist
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