How to calculate a percentage
- Percent of a number: multiply the number by the percentage divided by 100. 20% of 150 = 150 × 0.20 = 30.
- What percent one number is of another: divide the part by the whole and multiply by 100. 30 out of 150 = 30 / 150 × 100 = 20%.
- Percent change: subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 - 80) / 80 × 100 = 25% increase.
- Discount: multiply the price by the discount percentage to get the saving, then subtract it. 20% off $100 saves $20, so you pay $80.
Increases and decreases are not symmetric
A 50% increase followed by a 50% decrease does not return you to the start. $100 up 50% is $150, and $150 down 50% is $75. The second percentage is taken of a different base number.
Quick mental tricks
- 10% of a number: move the decimal point one place left.
- 5% is half of 10%, and 1% is the decimal point moved two places left.
- To find 15%, add 10% and 5%.
- For a 20% tip, find 10% and double it.
Common mistakes
- Mixing up which number is the whole. In "what percent is 30 of 150", the whole is 150.
- Adding percentages that apply to different base numbers.
- Confusing a percentage point change with a percent change. Going from 10% to 12% is 2 percentage points, but a 20% increase.
For detailed increase and decrease results, use the percent change calculator. For prices with tax, try the discount calculator.