The three percentage formulas
- X% of Y = X ÷ 100 × Y. Example: 15% of 80 = 12.
- A is what % of B = A ÷ B × 100. Example: 12 is 25% of 48.
- Percent change = (new − old) ÷ old × 100. Example: 50 → 65 is +30%.
Discounts and stacked discounts
A 25% discount on 80 costs 60. Two discounts do not add up: 20% off and then another 10% off is 28% off in total, not 30%. Use the Extra % off box to see the real total.
Percent vs percentage points
If an interest rate goes from 4% to 5%, it rose by 1 percentage point, which is a 25% increase. The % change tab gives the second number.
More percentage questions
- A is P% of what? Divide A by P ÷ 100. Example: 12 is 25% of 12 ÷ 0.25 = 48.
- Percentage difference compares two numbers with their average: |A − B| ÷ ((A + B) ÷ 2) × 100. 40 and 60 differ by 40%. Use it when neither number is the starting point.
Percentages in Excel and Google Sheets
Put the first number in A1 and the second in B1. % of a number: =A1/100*B1. What percent: =A1/B1*100. % change: =(B1-A1)/ABS(A1)*100. Each section above shows the formula for what you typed.
Worked examples from everyday life
- Tip: 18% of a $46.50 bill is 0.18 × 46.50 = $8.37, so you pay $54.87.
- Pay rise: a 3.5% raise on 52,000 a year is 52,000 × 1.035 = 53,820.
- Test score: 42 right out of 50 is 42 ÷ 50 × 100 = 84%.
- Weight loss: from 90 kg to 84 kg is (84 − 90) ÷ 90 × 100 = −6.7%.
- Price before tax: a price of 120 that includes 20% tax was 120 ÷ 1.20 = 100 before tax. Taking 20% off 120 gives 96, which is wrong, because the tax was added to 100, not to 120.
Why up and down are not the same
A price that rises from 80 to 100 goes up 25%. If it then falls back from 100 to 80, that is only a 20% fall, because the second change is measured from the bigger number. The same is true for investments: losing 50% needs a 100% gain to get back to where you started.
Percentage error
To check a measurement, use |measured − true| ÷ true × 100. If a recipe needs 250 g and you weigh 240 g, the error is 10 ÷ 250 × 100 = 4%. Type the true value and your value into the % difference or % change line and read the size of the result.
FAQ
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12.
How do I calculate percent increase?
Subtract the old value from the new value, divide by the old value and multiply by 100.
How do I work out a discount?
Multiply the price by (1 − discount ÷ 100). 25% off 80 is 80 × 0.75 = 60.
What is the difference between percentage change and percentage difference?
Percentage change measures from a starting value: 50 → 65 is +30%. Percentage difference compares two values with their average and has no direction: 50 and 65 differ by about 26%.
How do I calculate a percentage in Excel?
For X% of a number type =A1/100*B1. For what percent A is of B type =A1/B1*100, or =A1/B1 and format the cell as a percentage.
Why can a percentage be more than 100%?
Because the part can be bigger than the whole you compare it with. Going from 20 to 50 is a 150% increase, and 50 is 250% of 20.