The four percentage formulas
- X% of Y: X ÷ 100 × Y. 15% of 2,400 is 0.15 × 2,400 = 360.
- X is what percent of Y: X ÷ Y × 100. 360 is 360 ÷ 2,400 × 100 = 15% of 2,400.
- Percentage change: (new − old) ÷ old × 100. From 50 to 65 is 15 ÷ 50 × 100 = a 30% increase.
- Add or take off a percentage: Y ± (X% of Y). 2,400 plus 15% is 2,760.
Percentages aren't symmetric. A 50% increase followed by a 50% decrease doesn't bring you back where you started: 100 becomes 150, then 75.
Questions people ask
Why doesn't a 20% rise and a 20% fall cancel out?
Each percentage is taken from a different starting number. 100 + 20% is 120, but 120 − 20% is 96, because 20% of 120 is 24.
How do I find the original number before a percentage was added?
Divide by (1 + the percentage as a decimal). If 1,150 includes a 15% increase, the original was 1,150 ÷ 1.15 = 1,000. The VAT calculator does this for you.
What's the difference between percent and percentage points?
If a rate goes from 4% to 5%, that's a rise of 1 percentage point, but a 25% increase in the rate itself.