How percentages work
A percentage is a fraction out of 100. To find a percentage of a number, divide the percentage by 100 and multiply: 15% of 80 is (15 ÷ 100) × 80 = 12.
To find what percent one number is of another, divide the part by the whole and multiply by 100. For example, 18 is (18 ÷ 60) × 100 = 30% of 60.
To find percent change, subtract the old value from the new value, divide by the old value and multiply by 100. A positive result is an increase and a negative result is a decrease.
Common mistakes
- Using the wrong base. Percent change is always measured against the starting value. Going from 50 to 65 is a 30% increase, but going back from 65 to 50 is only a 23.08% decrease.
- Mixing up percent and percentage points. If a rate rises from 10% to 12%, it rose 2 percentage points, but the percent change is 20%.
- Forgetting to convert. 15% is 0.15 as a decimal, not 15.
Worked examples
What is 15% of 80?
= 12
(15 ÷ 100) × 80 = 12.
18 is what percent of 60?
= 30.00%
(18 ÷ 60) × 100 = 30%.
Percent change from 50 to 65
= 30.00%
(65 − 50) ÷ 50 × 100 = 30%, an increase.
Percent change from 80 to 60
= -25.00%
(60 − 80) ÷ 80 × 100 = −25%, a decrease.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 18 out of 60 is 18 ÷ 60 × 100 = 30%.
How is percent change calculated?
Subtract the old value from the new value, divide by the old value and multiply by 100. A negative answer means the value decreased.
Why does percent change differ depending on the direction?
Because the starting value is different. A rise from 50 to 65 is +30%, but a fall from 65 back to 50 is −23.08%, since the percentage is taken of 65 instead of 50.
Does this calculator round?
Percentages are shown to two decimal places. A percentage of a number is shown as calculated.