The three modes
X% of Y — simple multiplication. 15% of 240 = (15/100) × 240 = 36.
% Change — the percent increase or decrease from one number to another. Formula: ((B − A) / |A|) × 100.
X is Y% — find what percentage one number is of another. Formula: (X / Y) × 100.
Step-by-step examples
Percent of a number: what is 15% of 240?
- Turn the percentage into a decimal: 15 ÷ 100 = 0.15.
- Multiply: 0.15 × 240 = 36.
Percentage change: your electricity bill went from $1,250 to $1,100 over a year.
- Find the difference: 1,100 − 1,250 = −150.
- Divide by the starting value: −150 ÷ 1,250 = −0.12.
- Multiply by 100: −12%, a 12% decrease.
What percent: you scored 45 out of 60 on a test.
- Divide the part by the whole: 45 ÷ 60 = 0.75.
- Multiply by 100: 75%.
Quick reference: common percentages
| Percent | of 20 | of 50 | of 80 | of 200 | of 1,000 |
|---|---|---|---|---|---|
| 5% | 1 | 2.5 | 4 | 10 | 50 |
| 10% | 2 | 5 | 8 | 20 | 100 |
| 15% | 3 | 7.5 | 12 | 30 | 150 |
| 20% | 4 | 10 | 16 | 40 | 200 |
| 25% | 5 | 12.5 | 20 | 50 | 250 |
| 50% | 10 | 25 | 40 | 100 | 500 |
| 75% | 15 | 37.5 | 60 | 150 | 750 |
A handy trick: X% of Y equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
Mistakes to avoid
- Dividing by the wrong number. Percentage change always divides by the starting value. From 40 to 52 is a 30% increase, but from 52 back to 40 is a 23.08% decrease.
- Adding percentages that stack. Two 10% increases in a row are a 21% increase, not 20%, because 1.10 × 1.10 = 1.21.
- Mixing up percent and percentage points. If a rate rises from 4% to 5%, it rose by 1 percentage point, which is a 25% increase in the rate itself.
- Undoing a discount the wrong way. If a price after 20% off is $64, the original was $64 ÷ 0.80 = $80, not $64 × 1.20 = $76.80.
When the starting value is negative, the calculator divides by its absolute value so the sign of the result shows the direction of the change. Going from −50 to −25 shows +50%, because the value went up.