How to calculate percentages in your head
Tips, discounts, tax, test scores, "is this a good deal?" — nearly every percentage you meet in daily life can be done in two or three mental steps from a handful of building blocks.
The building blocks: 10%, 5% and 1%
- 10% — move the decimal point one place left. 10% of 64 is 6.4.
- 5% — half of 10%. 5% of 64 is 3.2.
- 1% — move the decimal point two places left. 1% of 340 is 3.4.
- 50%, 25% — halve, then halve again. 25% of 36 is 9.
Everything else is a combination:
15% of 64 = 10% + 5% = 6.4 + 3.2 = 9.6 20% of 85 = 10% × 2 = 8.5 × 2 = 17 35% of 80 = 10% × 3 + 5% = 24 + 4 = 28 18% of 42 = 10% + 8 × 1% = 4.2 + 3.36 = 7.56Tipping
For 15%, take 10% and add half of it again. For 20%, double 10%. For 18%, take 20% and knock a little off. On a $42 bill: 10% is $4.20, so 15% is $6.30 and 20% is $8.40.
The swap trick
x% of y is the same as y% of x. When one direction is awkward, flip it.
8% of 25 = 25% of 8 = 2 4% of 75 = 75% of 4 = 3 12.5% of 48 = 48% of 12.5 … or just ⅛ of 48 = 6Fractions you should recognise
| % | 50 | 25 | 20 | 12.5 | 10 | 33⅓ | 66⅔ | 75 |
|---|---|---|---|---|---|---|---|---|
| fraction | ½ | ¼ | ⅕ | ⅛ | 1⁄10 | ⅓ | ⅔ | ¾ |
Discounts
To find a sale price, work out what's left rather than what's taken off: 30% off means you pay 70%. On $60, 10% is $6, so 70% is $42.
Working backwards — "it's $120 after 20% off, what was the original?" — divide by what's left: $120 ÷ 0.8 = $150.
Percentage change
Change divided by the starting value. From 45 to 54 is a change of 9, and 9 is ⅕ of 45 — a 20% increase. Note that going back down from 54 to 45 is not 20%: the same 9 is only about 16.7% of 54.
Get the arithmetic underneath fast
Every percentage method above ends in a small multiplication, division or addition. If those are automatic, percentages are too. R3CK0N doesn't have a dedicated percentage drill; its multiplication and division drills train the arithmetic they rest on.
Drill multiplication