Percentage formulas
X% of Y = Y × X ÷ 100
Ratio = part ÷ total × 100
Change = (final − starting) ÷ starting × 100
Ratio = part ÷ total × 100
Change = (final − starting) ÷ starting × 100
Finding a percentage of a number
To find 15% of 200, multiply 200 by 15, then divide by 100: the answer is 30. A mental math trick: 10% of any number is found by moving the decimal point one place to the left. 15% = 10% + half of 10%.
Finding what percent one number is of another
Divide the part by the total, then multiply by 100. If you scored 30 out of 120, your result is 30 ÷ 120 × 100 = 25%.
Calculating an increase or decrease
Subtract the starting value from the final value, divide by the starting value and multiply by 100. A price going from $80 to $100 has increased by 25%. Careful: a 25% drop followed by a 25% increase doesn't bring you back to where you started. $100 minus 25% is $75, and $75 plus 25% is only $93.75.
Common percentages
| Percentage | Fraction | Decimal |
|---|---|---|
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.1 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.2 |
| 25% | 1/4 | 0.25 |
| 33.33% | 1/3 | 0.333 |
| 50% | 1/2 | 0.5 |
| 75% | 3/4 | 0.75 |