Percentages made easy: how to work out any percentage

What does per cent mean?

Per cent means “out of 100”. The word comes from the Latin per centum, “for each hundred”. It’s the same “cent” as in century (100 years) and centimetre (a hundredth of a metre).

So 18% just means 18 out of every 100. If you cut something into 100 equal pieces, 18% is 18 of those pieces. That’s why a percentage is really a fraction with 100 on the bottom: 18% = ¹⁸₁₀₀.

Money makes it click. There are 100 pennies in £1, so each penny is 1% of a pound. 50p is 50% of £1, 25p is 25%, and 10p is 10%.

The building blocks

A few percentages are really easy to work out. Learn these and you can build almost any other percentage from them. Here they are for 240:

10% is the most useful block of all. To divide by 10, every digit moves one place to the right: 240 becomes 24, and 75 becomes 7.5.

Three ways to work out a percentage of a number

There’s no single right way. Pick the one that suits the numbers.

Going further (ages 11+)

Did you know?

• Where % comes fromItalian merchants wrote “per cento”. Over time the “per” was dropped and “cento” shrank to two little circles with a line between them: %.
• Roman percentagesLong before decimals, the Roman emperor Augustus charged a tax of one hundredth (1%) on goods sold at auction.
• Up 25%, down 20%If £100 goes up 25% it becomes £125. To get back to £100 it only has to fall by 20%, because 20% of £125 is £25.
• Up and down don’t cancel£200 up 10% is £220. Then 10% off gives £198, not £200.
• More than 100%A 100% increase means the amount has doubled. A 200% increase means it is three times as big.
• Per milleThere’s a cousin of per cent: per mille (‰) means “out of 1,000”.

Fractions, decimals and percentages

These are three ways of writing the same amount. Learning the common ones by heart makes everything quicker.

Tips for teaching percentages

For parents. If your child is stuck, it’s usually one of the first three.

1. Start from half and a quarter. Even young children know half and a quarter. 50% is just another name for half, and 25% is a quarter. Begin there, not with a formula.
2. Make sure “divide by 10” is solid. 10% is the key building block. If moving digits for ÷10 and ÷100 is shaky, practise that first, and the rest falls into place.
3. Colour a 100 square. Seeing 37 squares out of 100 makes “37%” real. Print the colour-the-percentage worksheets below.
4. Use money. 100p in a pound turns every amount into a percentage: 30p is 30% of £1.
5. Let them choose a method. Building blocks for mental maths, fractions for friendly percentages, “multiply then ÷100” for awkward ones. Children who can do it two ways can check themselves.
6. Find 1% and scale up. If a number feels hard, work out 1% (divide by 100), then multiply by the percentage you need. This always works.
7. Estimate before calculating. “Is the answer more or less than half? More or less than a tenth?” It catches most slips straight away.
8. Spot them in real life. Sale signs, the phone battery, a “70% chance of rain”, test scores, the sugar on a food label. Ask “What’s 20% off that?” in the shop.
9. Show the swap trick. It feels like magic (8% of 25 = 25% of 8 = 2) and gets reluctant children interested.
10. Little and often. Ten minutes of percentages twice a week beats one long session. Roll a fresh worksheet each time.

What do children learn, and when?

In England, the National Curriculum builds up to percentages step by step:

1. Year 1 (5–6)Find a half and a quarter of a shape, an object or an amount, by sharing into 2 or 4 equal parts.
2. Year 2 (6–7)Find ⅓, ¼, ²⁄₄ and ¾ of shapes, lengths, groups and amounts, and know that ²⁄₄ is the same as ½.
3. Year 3 (7–8)Count in tenths, and learn that a tenth is one of 10 equal parts. This is where 10% starts.
4. Year 4 (8–9)Hundredths, dividing by 10 and 100, and knowing that ¼, ½ and ¾ are 0.25, 0.5 and 0.75.
5. Year 5 (9–10)Meet the % sign: per cent means “parts per 100”. Write percentages as fractions over 100 and as decimals, and know the percentages for ½, ¼, ⅕, ⅖ and ⅘.
6. Year 6 (10–11)Work out percentages of amounts (such as 15% of 360), compare things using percentages, and know the common fraction, decimal and percentage equivalents.
7. Key Stage 3 (11–14)One amount as a percentage of another, percentages over 100%, percentage increase and decrease, finding the original amount, simple interest, and using multipliers like × 1.15.
8. Key Stage 4 (GCSE)Repeated percentage change, growth and decay, and compound interest.

Paraphrased from the National Curriculum for England. Schools only have to cover each key stage’s content by the end of that key stage, so the exact year can vary. Calculators are meant to come in near the end of Year 6, once written and mental methods are secure.