Learn the fast percentage shortcuts used by accountants and shoppers, plus formulas for discounts, tax, percentage change, and tipping.
Percentages show up everywhere — sales tax, restaurant tips, shopping discounts, loan interest, exam scores, growth rates. The math is simple, but most people reach for a calculator out of habit instead of doing it in their head. A handful of shortcuts will let you do the same work mentally in about two seconds.
Percentage OF a number: (percentage ÷ 100) × number
So 20% of 150 is 0.20 × 150 = 30. That is the one formula you actually need. Every trick below is just a faster way to do that same multiplication without writing anything down.
10% of any number is just that number with the decimal moved one place to the left.
Once you have 10%, you can get most other percentages by combining. 5% is half of 10%. 20% is double. 15% is 10% plus half of 10%. 30% is three lots of 10%.
X% of Y is always the same as Y% of X. This is a genuine mathematical identity, and it makes some problems trivial.
For a 23% tip on $40, split it: 20% ($8) + 3% ($1.20) = $9.20. You calculated two easy numbers instead of one hard one.
When something goes from an old value to a new value, the percentage change is:
((new − old) ÷ old) × 100
If a stock goes from $40 to $50, the change is (50 − 40) ÷ 40 = 0.25, so +25%. If it falls from $50 to $40, the change is (40 − 50) ÷ 50 = −0.20, so −20%. Notice the percentages are not symmetric — a 25% gain followed by a 20% loss brings you back where you started.
A 30% off sale means you pay 70% of the original. Rather than calculating the discount and subtracting, just multiply by 0.70 directly.
An item at $80 with 30% off: 80 × 0.70 = $56. One step instead of two.
For tipping, most people use 15–20%. For 18%, find 10% + 10% and take the average.
For sales tax, the same approach works. 7.5% tax on $60? That is 7% + 0.5%. 7% of 60 = 4.20, 0.5% = 0.30, total tax = $4.50.
Percentages only feel hard because schools teach them abstractly. In real life, nearly every useful percentage calculation can be done in your head by finding 10% and building from there. Try the tricks on tomorrow's coffee receipt — you will stop reaching for your phone within a week.