Most percentages are easy to calculate in your head once you start from 10%. Moving the decimal point one place to the left gives 10% of any number, halving that gives 5%, and moving the point two places gives 1%. Almost every percentage you meet in a shop, a restaurant or on a payslip is built from those three.
It is also the way maths is taught in English schools. Pupils learn percentage and decimal equivalents in primary school, then work with percentage changes at secondary level. This guide gathers the anchors, the shortcuts for the percentages you meet most, increases and decreases, VAT at 20% and a short routine to keep it all quick.
The three anchors: 10%, 5% and 1%
Every quick method rests on three moves. To find 10%, divide by 10: move the decimal point one place to the left, so 10% of 80 is 8 and 10% of 4.50 is 0.45. To find 5%, take half of that 10%. To find 1%, divide by 100: move the point two places, so 1% of 80 is 0.80.
Dividing by 10 is the 10 times table read backwards, which is why it feels so easy. From these three anchors you can build almost any percentage by adding, doubling or halving. The table below gives the most common ones, worked out on 80.
| Percentage | How to get it | Example: 80 |
|---|---|---|
| 50% | Halve the number | 40 |
| 25% | Halve it twice | 20 |
| 10% | Move the decimal point one place | 8 |
| 5% | Half of 10% | 4 |
| 1% | Move the decimal point two places | 0.80 |
| 15% | 10% plus 5% | 12 |
| 20% | 10% doubled | 16 |
| 75% | The number minus 25% | 60 |
Percentage tricks for the numbers you meet most
A few shortcuts save time in everyday situations. 20% is a fifth, so you can also divide by 5, which is the 5 times table in reverse: 20% of 45 is 9. 25% is a quarter: 25% of 36 is 9. 12.5% is an eighth, or half of 25%: 12.5% of 64 is 8.
The most useful trick is that a percentage can be swapped. x% of y is always equal to y% of x, because both are x times y divided by 100. So 8% of 25 is the same as 25% of 8, which is 2, and 4% of 75 is 75% of 4, which is 3. When one side of the sum looks awkward, try the other.
For odd percentages, split them into anchors. 17% of 200 is 10% (20) plus 5% (10) plus 2% (4), which makes 34. 9% of 300 is 10% (30) minus 1% (3), which makes 27. With a little practice, the split becomes automatic and you stop reaching for your phone.
It also helps to know a handful of fraction equivalents by heart. Pupils in England are expected to recall equivalences between simple fractions, decimals and percentages by the end of Year 6, and the same handful serves adults well: a half is 50%, a quarter 25%, three quarters 75%, a fifth 20%, a tenth 10% and an eighth 12.5%. A third is about 33.3%. Each one turns a percentage into a simple division, which is often the fastest route of all.
When an exact answer is not needed, round first. 18% of 49 is close to 20% of 50, so a little under 10; the exact figure is 8.82. Estimating before you calculate also catches mistakes, on a receipt or in your own sums, because a result far from the estimate is a signal to check again.
How to work out 15 percent, 20 percent and 12.5 percent
These three cover most bills. For 15% on a restaurant bill of £48: 10% is £4.80, 5% is £2.40, together £7.20. For a 20% discount on a £35 jacket: 10% is £3.50, doubled £7, so you pay £28. For a 12.5% service charge on £64: 10% is £6.40 and 2.5% is a quarter of that, £1.60, together £8.
When you only need the final price, multiply by what remains. A 20% discount leaves 80%, so £35 × 0.8 = £28. A 15% tip on top of £48 is 115% of the bill: £48 + £7.20 = £55.20. Thinking in terms of what is left, or what is added, saves a subtraction at the end and gives you the figure you actually need at the till.
Percentage increase and decrease without a calculator
A percentage change is a multiplication. A 10% rise multiplies by 1.1, a 10% fall by 0.9, a 25% fall by 0.75. This is how the national curriculum for England asks Key Stage 3 pupils to read percentage changes: as decimals, multiplicatively. It makes repeated changes easy to follow.
It also explains a classic trap. A price that rises by 10% and then falls by 10% does not come back to where it started: 100 becomes 110, and 10% of 110 is 11, which leaves 99. Overall, 1.1 × 0.9 = 0.99, a 1% fall. In the same way, two rises of 10% make 21%, because 1.1 × 1.1 = 1.21.
| Change | Multiply by | Example on 50 |
|---|---|---|
| +50% | 1.5 | 75 |
| +20% | 1.2 | 60 |
| +10% | 1.1 | 55 |
| +5% | 1.05 | 52.50 |
| −5% | 0.95 | 47.50 |
| −10% | 0.9 | 45 |
| −20% | 0.8 | 40 |
| −25% | 0.75 | 37.50 |
Add or remove VAT at 20 percent
In the UK, the standard rate of VAT is 20%. There is a reduced rate of 5% for some goods and services, such as home energy and children's car seats, and a zero rate for most food and children's clothes, according to the VAT rates page on GOV.UK. Adding 20% is easy: find 10%, double it, add it on. £45 plus VAT is £45 + £9 = £54.
Removing it is where people slip. Taking 20% off a price that includes VAT gives the wrong answer, because the VAT was calculated on the smaller price before VAT. The rule to remember is that VAT at 20% is one sixth of a price that includes it. On £54, a sixth is £9, so the price before VAT is £45. On £60, the VAT is £10 and the price before VAT is £50; taking 20% off £60 would give £48, which is wrong by £2.
Practise percentages in your head, ten minutes a day
Speed comes from repetition. A short daily routine works better than a long session once a week: start with the anchors on round numbers, then move to prices you actually see, a receipt, a sale sign, a payslip. Say the steps out loud the first few times, then only the answer.
- Days 1 to 3. 10%, 5% and 1% of ten random numbers a day.
- Days 4 to 6. 15%, 20% and 25%, built from the anchors.
- Days 7 to 10. Increases and decreases with the multipliers, then VAT in both directions.
Keep a list of the ones you get wrong and redo them the next day, then a few days later. That is spaced repetition, and it is how Kalc trains percentages, one of its eight skills, in sessions of about ten minutes. If the arithmetic behind it still feels slow, the times tables from 2 to 12 are the place to start.
Frequently asked questions
How do you work out 15 percent of a number in your head?
Find 10% by moving the decimal point one place to the left, then add half of it for the 5%. On £60, that is £6 plus £3, so £9.
What is the quickest way to take 20 percent off a price?
Multiply by 0.8, or find 10%, double it and subtract. On £35, 10% is £3.50 and 20% is £7, so the price becomes £28.
How do you remove VAT at 20 percent from a price?
Divide the price by 1.2. VAT at 20% is one sixth of a price that includes it: on £60, the VAT is £10 and the price before VAT is £50.
Why does a 10 percent rise followed by a 10 percent fall not bring a price back?
Because the fall applies to a bigger number. 100 rises to 110, and 10% of 110 is 11, which leaves 99: overall, a 1% fall.
Is 8 percent of 25 the same as 25 percent of 8?
Yes. x% of y always equals y% of x, because both are x times y divided by 100. Both give 2, and the second is much easier to see.
Practise mental maths in Kalc
Ten minutes a day, adapted to your level, with spaced repetition bringing back what you miss.