What is X% of Y?
Divide the percentage by 100 and multiply. 15% of 80 = 0.15 × 80 = 12. A quick way to find 10% is to move the decimal point one place left; 5% is half of that.
X is what percent of Y?
Divide X by Y and multiply by 100. 18 out of 24 = 18 ÷ 24 × 100 = 75%.
Percentage change
Subtract the old value from the new one, divide by the old value and multiply by 100. A price going from 40 to 50 is (50 − 40) ÷ 40 × 100 = 25% more. From 50 back to 40 is a 20% decrease, because the starting point is now larger.
Adding or removing a percentage
- Add 20%: multiply by 1.2. 50 × 1.2 = 60.
- Take 20% off: multiply by 0.8. 50 × 0.8 = 40.
- Find the price before 20% tax was added: divide by 1.2. 60 ÷ 1.2 = 50.
Percent vs percentage points
If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but by 25% in relative terms. News reports often mix the two up.
Skip the maths
The Percentage Calculator does all three calculations as you type.
Finding the original before a change
If a price is 60 after 25% off, the original is not 60 + 25%. The 60 is 75% of the original, so divide: 60 ÷ 0.75 = 80. Adding 25% to 60 gives 75, which is wrong.
Changes in a row
- Up 10%, then down 10%: 1.1 × 0.9 = 0.99, a 1% loss, not back to the start.
- 20% off, then another 10% off: 0.8 × 0.9 = 0.72, which is 28% off, not 30%.
- 10% growth for three years: 1.1 × 1.1 × 1.1 = 1.331, a 33.1% rise, not 30%.
Multiply the factors; never add the percentages.
Common mistakes
- Dividing by the wrong number. Percentage change is always divided by the starting value. From 80 to 100 is a 25% rise; from 100 to 80 is a 20% fall.
- A change from zero. Going from 0 to 5 has no percentage change, because you cannot divide by zero. Give the actual numbers instead.
- Averaging percentages. 50% of 10 people and 10% of 1,000 people is not 30% overall; it is 105 of 1,010, or 10.4%.