How to calculate percentages
"Percent" means "per hundred", so every percentage question comes down to one of three formulas. The tool above runs all three; here is what each one does, so you can check the answer or work it out by hand.
1. X% of a number
result = (X ÷ 100) × number
Example: a 20% tip on a £45 bill is 0.20 × 45 = £9.
2. What percent one number is of another
percent = (part ÷ whole) × 100
Example: scoring 42 out of 60 on a test is 42 ÷ 60 × 100 = 70%.
3. Percentage increase or decrease
change = (new − old) ÷ |old| × 100
Example: rent going from $1,200 to $1,320 a month is (1,320 − 1,200) ÷ 1,200 × 100 = a 10% increase. If the result is negative, it's a decrease.
Common mistakes
- Percentage change vs percentage points. An interest rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate itself.
- Reversing a percentage. If a price after 20% off is $80, the original was 80 ÷ 0.8 = $100 — not $80 + 20% = $96.
- Stacking discounts. 20% off and then another 10% off is 28% off in total, not 30%, because the second discount applies to the already-reduced price.