Guide
How to calculate percentages in your head
Build any percentage from 10% and 5%, use the commutative trick, and check restaurant bills and discounts without a calculator.
Almost every percentage worth doing in your head can be built from two pieces: 10% and 5%. Once you can produce those instantly, the rest is addition.
The two building blocks
| Want | Do this | On 240 | On 86 |
|---|---|---|---|
| 10% | Move the decimal one place left | 24 | 8.6 |
| 5% | Half of 10% | 12 | 4.3 |
| 1% | Move the decimal two places left | 2.4 | 0.86 |
That is the entire method. Everything below is assembling these three.
Building the common percentages
| Percentage | Build from | On 240 |
|---|---|---|
| 5% | Half of 10% | 12 |
| 15% | 10% + 5% | 24 + 12 = 36 |
| 20% | 10% doubled | 48 |
| 25% | Quarter — halve it twice | 60 |
| 30% | 10% × 3 | 72 |
| 35% | 10% × 3 + 5% | 72 + 12 = 84 |
| 40% | 10% × 4 | 96 |
| 60% | Half + 10% | 120 + 24 = 144 |
| 75% | Whole − quarter | 240 − 60 = 180 |
| 90% | Whole − 10% | 240 − 24 = 216 |
Note the pattern at the top end: for anything above 50%, subtract from the whole rather than adding up. 90% of a number is easier as "minus 10%" than as "nine lots of 10%".
The trick nobody teaches
x% of y equals y% of x. Percentages commute, because both are the same multiplication written in a different order.
| Looks hard | Flip it | Answer |
|---|---|---|
| 4% of 75 | 75% of 4 | 3 |
| 8% of 50 | 50% of 8 | 4 |
| 16% of 25 | 25% of 16 | 4 |
| 12% of 50 | 50% of 12 | 6 |
| 3% of 200 | 200% of 3 | 6 |
Whenever one of the two numbers is a friendly fraction — 25, 50, 20, 200 — flip so that number does the work.
Restaurant bills
For a 20% tip: move the decimal one place and double. On $47.30 → $4.73 → $9.46, call it $9.50.
For 18%: get 20%, then subtract a tenth of that figure. $9.46 − $0.95 = $8.51.
For 15%: 10% plus half of it. $4.73 + $2.37 = $7.10.
Splitting between four people at 20%: work out the total with tip, then halve it twice. $47.30 + $9.46 = $56.76, halve to $28.38, halve again to $14.19 each.
Discounts
Discounts are easier calculated as what you pay rather than what you save, because it is one step instead of two.
| Sign says | You pay | On $80 |
|---|---|---|
| 10% off | Whole − 10% | $72 |
| 20% off | Whole − double 10% | $64 |
| 25% off | Three quarters | $60 |
| 30% off | Whole − triple 10% | $56 |
| 33% off | Two thirds | $53.33 |
| 40% off | 60% — half plus 10% | $48 |
| 60% off | 40% — 10% × 4 | $32 |
| 70% off | Three tenths | $24 |
For stacked discounts, do them one at a time. "50% then 20%": halve $80 to $40, then take 20% off ($8) to reach $32. Never add the percentages together — that would give 70% off and an answer of $24, which is wrong by eight dollars.
VAT and sales tax
Adding 20% VAT: take 10%, double it, add. £45 → £4.50 → £9 → £54.
Removing 20% VAT is the one people get wrong. You divide by 1.2, not subtract 20%. The mental shortcut is to divide by 6 and subtract: £54 ÷ 6 = £9, and £54 − £9 = £45. This works because 1/6 of a VAT-inclusive price is exactly the VAT when the rate is 20%.
For 5% VAT, the equivalent shortcut is to divide by 21. For US sales tax at 8%, adding is 10% minus a fifth of that: $60 → $6 → minus $1.20 → $4.80 of tax.
Percentage change between two numbers
Find the gap, then ask what fraction of the starting number it is.
From 40 to 50: the gap is 10, and 10 out of 40 is a quarter, so 25% up.
From 50 to 40: the gap is still 10, but now it is 10 out of 50, so 20% down.
The asymmetry is the whole point and the most common error in the topic. Always divide by where you started.
Sanity checks
- Half rule. Anything above 50% must be more than half the number. If 60% of 80 comes out at 40, something went wrong.
- Double rule. 20% is exactly double 10%. If they are not, recheck.
- Order of magnitude. 15% of a number is roughly a seventh of it. 15% of 350 should be near 50.
- The reversal trap. A 20% rise followed by a 20% fall does not return you to the start — $100 becomes $120, then $96.
Practice ladder
Work these without writing anything down. Answers in order: 12, 27, 45, 9, 4, 34, 25% up.
- 15% of 80
- 30% of 90
- Tip of 18% on a $250 bill
- 7% of 128, to the nearest whole number
- 16% of 25
- A £170 item with 20% off
- Percentage change from 60 to 75
Check your answer
Open the Percentage Calculator