What a percentage means
“Per cent” means “per hundred”. 25% is 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25. Converting a percentage to a decimal (divide by 100) is the key to every percentage calculation.
1. Find X% of a number
Formula: X ÷ 100 × number. Example: a 15% tip on a bill of 80 is 15 ÷ 100 × 80 = 12.
2. What percent is one number of another?
Formula: part ÷ whole × 100. Example: 42 correct answers out of 50 is 42 ÷ 50 × 100 = 84%.
3. Percentage increase or decrease
Formula: (new − old) ÷ old × 100. Example: sales rising from 200 to 250 is (250 − 200) ÷ 200 × 100 = +25%. Falling from 250 to 200 is −20% — not −25%, because the starting value is different.
4. Add or subtract a percentage
Formula: number × (1 ± X ÷ 100). Example: adding 20% VAT to 50 gives 50 × 1.2 = 60. A 30% discount on 60 gives 60 × 0.7 = 42.
Common mistakes
- Adding percentages from different bases: +10% then −10% does not return to the start (100 → 110 → 99).
- Stacking discounts: 20% off and then 10% off is 28% off, not 30%.
- Confusing percentage points with percent: a rate rising from 4% to 5% is 1 percentage point, but a 25% increase.
- Calculating change from zero, which is undefined.
Worked examples from everyday life
- Salary rise: from 2,500 to 2,700 is (2,700 − 2,500) ÷ 2,500 × 100 = 8%.
- Exam score: 68 out of 80 is 68 ÷ 80 × 100 = 85%.
- Restaurant tip: 12% of 45 is 45 × 0.12 = 5.40.
- Price before tax: 119 including 19% VAT was 119 ÷ 1.19 = 100.
Percentages in spreadsheets
In Excel or Google Sheets, a percentage of a number is =A1*20%, the percentage one value is of another is =A1/B1 formatted as a percentage, and the change between two values is =(B1-A1)/A1. These are the same formulas the calculator uses, so you can check your spreadsheet results quickly.
Let the calculator do it
The Percentage Calculator handles all four cases, shows the formula with your numbers, and warns you when a result is undefined. For prices, the Discount Calculator handles stacked discounts and tax, and the Profit Margin Calculator explains margin versus markup.
Frequently asked questions
How do I calculate a percentage in my head?
Find 10% by moving the decimal point one place left, then multiply. 30% of 70: 10% is 7, so 30% is 21.
How do I reverse a percentage increase?
Divide by (1 + X ÷ 100). A price of 120 including 20% tax was 120 ÷ 1.2 = 100 before tax.
Can a percentage be over 100?
Yes. If a value doubles, it has increased by 100%; if it triples, by 200%.