Almost every percentage you will ever need can be done in your head in about two seconds, and the whole method fits in one sentence: find 10%, then build. 10% of anything is that number with the decimal point moved one place left. From there, 5% is half of it, 1% is a tenth of it, 20% is two of them, and 35% is three of them plus a half. No calculator, no formula, and no reaching for a phone in a restaurant.
Move the decimal point one place to the left. 10% of 60 is 6. 10% of 847 is 84.7. 10% of 25 is 2.5. That is the only move you have to be able to do instantly, and everything else is built on it.
20% — two lots of 10%.
30% — three lots.
5% — half of 10%.
15% — 10% plus half of it.
1% — a tenth of 10%, or the decimal point moved two places.
2.5% — a quarter of 10%.
That covers nearly everything in daily use. 35% of 60: 10% is 6, three of them is 18, half of 6 is 3, total 21. Two seconds, and no step in it is harder than halving.
This is the trick most people never learn, and it collapses a whole category of awkward questions. x% of y is always the same as y% of x.
8% of 50 looks unpleasant. 50% of 8 is obviously 4. Same answer, because both are 8 × 50 ÷ 100 — the multiplication does not care which number came first.
So 4% of 75 becomes 75% of 4, which is 3. 16% of 25 becomes 25% of 16, which is 4. Whenever one of the two numbers is friendly — 50, 25, 10, 20 — flip it and take the easy route.
If a percentage looks hard, swap the two numbers. One of the two versions is nearly always trivial.
Discounts: work out what you pay
30% off means you pay 70%. Finding 70% directly is one step; finding 30% and subtracting it is two, and the second step is where the mistakes happen. 30% off £45 is 70% of 45, which is 10% (4.50) seven times, so £31.50.
Two discounts do not add
An extra 20% off an already 30%-off price is not 50% off. It is 70% then 80% of that, which is 56% of the original — a 44% discount, not 50%. Percentages applied one after another multiply.
Tips
10% then half again gives 15%. 10% doubled gives 20%. On a £64 bill: 10% is 6.40, half of that is 3.20, so 15% is £9.60.
Tax on top
Adding 20% tax means multiplying by 1.2. Removing it means dividing by 1.2, not subtracting 20% — subtracting takes 20% of the bigger number and leaves you short. From £120 including 20% tax, the pre-tax figure is 120 ÷ 1.2 = £100, and the tax was £20, not £24.
A percentage change is always measured against the starting value. Subtract the old from the new, divide by the old, multiply by 100.
40 to 50 is an increase of 10 on a base of 40, which is 25%. But 50 back to 40 is a decrease of 10 on a base of 50, which is 20%. The same ten, two different percentages, because the base changed.
That asymmetry has real consequences. Something that falls 50% needs to double — a 100% rise — to get back. And 'prices rose 10% then fell 10%' leaves you 1% down: 100 becomes 110, then 10% of 110 is 11, leaving 99.
It is also why 'percentage points' exists as a phrase. A rate going from 4% to 5% is a rise of one percentage point and a rise of 25 percent, and mixing those up is the most common statistic error in the news.
If 20 is 25% of something, the whole is 80. The general method: divide by the percentage, multiply by 100. Or, more easily, recognise that 25% means a quarter, so the whole is four times as big.
Reverse questions are the ones people most often get backwards, usually by taking a percentage of the wrong number. The check is to run it forwards: if the answer is 80, then 25% of 80 should be 20. It is.
The Percentage Calculator shows the working for all three question types, so you can see which route it took rather than just the number.
Percentages are one of the few bits of school arithmetic that genuinely show up every week — in shops, on bills, in pay, in the news. The difference between someone who does them in their head and someone who does not is almost entirely practice, not ability.
The route is the same as for any other fact: short, shuffled, daily. Percent Drill runs sixty seconds of them and shows the 10%-based route whenever you miss one.
Find 10% by moving the decimal point one place left, then build from it. 5% is half of it, 1% is a tenth of it, and 35% is three lots plus a half.
Take 10%, then add half of it. On 64: 10% is 6.40, half is 3.20, so 15% is 9.60.
Because x% of y and y% of x are the same multiplication written in a different order. 8% of 50 and 50% of 8 both come to 4.
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 40 to 50: 10 ÷ 40 = 0.25, so a 25% increase.
Divide by 1.2, do not subtract 20%. From £120 including 20% tax, the pre-tax figure is 120 ÷ 1.2 = £100.
No. 30% off then a further 20% off is 70% then 80% of that, which is 56% of the original — a 44% discount, not 50%.
Find 10%, build from it, and flip the awkward ones. That is the whole method, and it covers tips, discounts, tax and most of the statistics in the news. Check your working on the [Percentage Calculator](/tools/percentage-calculator), then get it to automatic on [Percent Drill](/games/percent-drill).