Percentages show up everywhere: sale tags, exam results, interest rates, pay rises and nutrition labels. The good news is that you only need three formulas, and once you understand why they work, you can do most percentage maths in your head.
What a percentage really is
"Percent" means "out of 100". So 35% is just 35 out of every 100, or 0.35 as a decimal. Almost every percentage problem comes down to converting between a percentage, a decimal and a fraction.
Formula 1: Find a percentage of a number
Turn the percentage into a decimal and multiply. To find 15% of 240, work out 0.15 × 240 = 36. A shop that takes 15% off a 240 item is giving you a 36 discount.
Formula 2: Find what percent one number is of another
Divide the part by the whole, then multiply by 100. If you answered 38 of 50 questions correctly, then 38 ÷ 50 = 0.76, so your score is 76%.
Formula 3: Find the percentage change
Subtract the old value from the new one, divide by the old value, then multiply by 100. If your rent goes from 800 to 860, the change is (860 − 800) ÷ 800 = 0.075, which is a 7.5% increase.
Three real-life examples
- Pay rise: a 4% raise on a salary of 3,000 a month adds 0.04 × 3,000 = 120, so the new salary is 3,120.
- Test marks: scoring 45 out of 60 gives 45 ÷ 60 × 100 = 75%.
- Price drop: a phone falls from 500 to 425. The change is (425 − 500) ÷ 500 = −15%.
Mistakes to avoid
- Using the wrong starting value. Always divide by the original number when calculating change.
- Adding successive percentages. A 20% increase then a 20% decrease leaves you 4% below where you started.
- Mixing up percent and percentage points. A rate moving from 5% to 7% rose by 2 percentage points, but by 40 percent.
Mental maths shortcuts
Find 10% by moving the decimal point one place left. Then build up: 20% is double that, 5% is half, and 15% is 10% plus 5%. For 1%, move the decimal two places.
When you want a quick check, use our free Percentage Calculator. If you are working with prices, our Discount Calculator handles stacked discounts and tax.
Frequently asked questions
Can a percentage be more than 100?
Yes. Something that has doubled has increased by 100%, and something that has tripled has increased by 200%.
How do I turn a fraction into a percentage?
Divide the top number by the bottom number and multiply by 100. For example, 3/8 = 0.375 = 37.5%.
This guide is for general information only. See our disclaimer.