Percentages in Your Head
The handful of tricks that cover almost every percentage you meet away from a keyboard — tips, discounts, tax and quick sanity checks — with the reasoning behind each one.
Start from 10%
Nearly all mental percentage work is built on one move: 10% of any number is that number with the decimal point shifted one place left. 10% of 86 is 8.6; 10% of 1,240 is 124. There is no arithmetic to do, only a point to move.
Everything else is scaling that one figure up or down:
| You want | From 10% | On 86 |
|---|---|---|
| 1% | Move the point again | 0.86 |
| 5% | Halve it | 4.30 |
| 15% | Add half of it | 12.90 |
| 20% | Double it | 17.20 |
| 25% | Double it, add half | 21.50 |
| 30% | Triple it | 25.80 |
| 40% | Quadruple it | 34.40 |
| 45% | Quadruple it, add half | 38.70 |
| 70% | Multiply by 7 | 60.20 |
| 90% | Subtract it from the total | 77.40 |
The last row is worth its own note: for high percentages, take the small complement and subtract. 90% of 86 is easier as 86 − 8.6 than as nine lots of 8.6, and 95% is 86 minus 4.30.
The reversal trick
X% of Y always equals Y% of X. This falls straight out of the formula — both are (X × Y) ÷ 100 — but it is not obvious until someone points it out, and it turns awkward problems into easy ones.
X% of Y = Y% of X
4% of 75 looks like work. Flipped, it is 75% of 4, which is 3. Similarly 12% of 50 becomes 50% of 12, which is 6; and 16% of 25 becomes 25% of 16, which is 4.
The trick pays off whenever one of the two numbers is a friendly percentage — 25, 50, 75 — or when one is much smaller than the other. Scan both directions before starting.
It also works as a sanity check. If you calculate 20% of 150 as 30, the reversal says 150% of 20 should also be 30. It is: 20 plus half of 20 again.
Benchmark fractions
Some percentages are fractions in disguise, and dividing is faster than multiplying by a decimal.
| Percentage | Is | So do this | On 240 |
|---|---|---|---|
| 12.5% | 1/8 | Halve three times | 30 |
| 16.7% | 1/6 | Divide by 6 | 40 |
| 20% | 1/5 | Divide by 5 | 48 |
| 25% | 1/4 | Halve twice | 60 |
| 33.3% | 1/3 | Divide by 3 | 80 |
| 37.5% | 3/8 | Divide by 8, times 3 | 90 |
| 62.5% | 5/8 | Divide by 8, times 5 | 150 |
| 66.7% | 2/3 | Divide by 3, double | 160 |
| 75% | 3/4 | Take a quarter off | 180 |
| 87.5% | 7/8 | Take an eighth off | 210 |
Halving is the cheapest operation there is, so anything on the eighths line — 12.5%, 37.5%, 62.5%, 87.5% — is faster as repeated halving than as a multiplication. Recognising 37.5% as three eighths turns an unpleasant sum into three halvings and a small multiplication.
Discounts, tips and tax in practice
A discount is what is left, not what comes off
Reading "35% off £68" as "find 35%, then subtract" is two operations. Reading it as "pay 65%" is one. 65% of 68 is 68 minus a third of 68 minus a fiftieth — or, more practically, 10% is 6.80, so 60% is 40.80 and 5% is 3.40, giving £44.20.
Round the bill, not the percentage
For a tip, round the bill to something friendly first and accept the small error. A £57.40 bill is £57 for mental purposes; 10% is £5.70, so 20% is £11.40. The rounding cost you four pence, which is not a number anyone is tracking.
Tax on a price tag
To add 20% mentally, add a fifth: £45 becomes £45 + £9 = £54. To take 20% out of a gross price, divide by 6 to get the tax: £54 ÷ 6 = £9, leaving £45. The "divide by 6" shortcut works only at 20%, but the equivalent exists at every rate — it is rate ÷ (100 + rate).
Sanity-check with a bracket
Before trusting any percentage, bracket it between two easy ones. If you need 43% of 380, note that 40% is 152 and 50% is 190, so the answer must sit between them and nearer the bottom. Getting 163.4 is plausible; getting 16.34 or 234 is not, and the bracket catches a misplaced decimal point instantly.
Two rules for growth
The rule of 72
Divide 72 by an annual growth rate to get roughly the number of years for something to double. At 6% a year, 72 ÷ 6 = 12 years. At 3%, 24 years. It is an approximation that holds well between about 4% and 12%, and it turns compound interest from a calculation into a fact you can state in conversation.
Small percentages roughly add
For changes under about 10%, chaining them is close to adding them: a 3% rise followed by a 4% rise is 7.12%, near enough to 7% for a mental estimate. Above 10% the approximation breaks down and you have to multiply — a 30% rise followed by a 40% rise is 82%, not 70%, and the gap only widens from there.
Frequently Asked Questions
- What is the fastest way to work out a percentage in my head?
- Find 10% by moving the decimal point one place left, then scale it. Halve it for 5%, double it for 20%, add half of it for 15%.
- Why does X% of Y equal Y% of X?
- Both work out to (X × Y) ÷ 100, so the order does not matter. It means 4% of 75 can be read as 75% of 4, which is 3.
- How do I calculate a 15% tip quickly?
- Take 10% of the bill, halve it for 5%, and add the two together. On a £64 bill: £6.40 + £3.20 = £9.60.
- What is the rule of 72?
- Dividing 72 by a growth rate gives roughly the years needed to double. At 6% a year, something doubles in about 12 years.
- How do I take 20% VAT out of a price in my head?
- Divide the gross price by 6 to get the tax. £54 ÷ 6 = £9, leaving £45 net.
- Can I just add two percentage changes together?
- Only for small ones. Under about 10% the error is negligible; a 30% and a 40% rise compound to 82%, not 70%.
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