Four everyday percentage questions answered instantly — percent of, what percent, percentage change and reverse percentage.
“Per cent” means per hundred. 25% is 25 out of every 100, or 25 ÷ 100 = 0.25. Almost every percentage problem you’ll meet in shopping, school, work or the news comes down to one of four formulas.
1. What is X% of Y?
Result = (X ÷ 100) × Y
- 15% of 200 = 0.15 × 200 = 30
- 8% sales tax on $45 = 0.08 × 45 = $3.60
- 20% tip on $62 = 0.2 × 62 = $12.40
Mental shortcut: 10% is the number with the decimal moved one place left; 1% moves it two places. Build anything from those. 17% of 300 = 10% (30) + 7 × 1% (21) = 51.
2. X is what percent of Y?
Percent = (X ÷ Y) × 100
- 30 out of 120 = 0.25 × 100 = 25%
- Scored 42 out of 50 = 84%
- $450 rent from a $1,800 income = 25% of income
The number after “of” is always the whole, and it goes on the bottom.
3. Percentage change from A to B
Change % = (B − A) ÷ |A| × 100
- Price rises $80 → $100: 20 ÷ 80 = +25%
- Price falls $100 → $80: −20 ÷ 100 = −20%
The base is always the starting value, which is why the two answers differ. This trips up a lot of people; Percentage Increase and Decrease: How to Calculate Change Correctly explains it in depth.
4. X is Y% of what? (reverse percentage)
Whole = X ÷ (Y ÷ 100)
- 45 is 30% of what? 45 ÷ 0.3 = 150
- You paid $63 after 30% off. You paid 70%, so 63 ÷ 0.7 = $90 originally.
- Price including 20% VAT is $96. Before VAT: 96 ÷ 1.2 = $80
A classic mistake is to subtract 20% from $96 to remove VAT, which gives $76.80, not $80.
Converting between fractions, decimals and percentages
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
To convert a decimal to a percent, multiply by 100. To convert a percent to a decimal, divide by 100.
Everyday uses
- Exams: marks as a percentage, and how negative marking changes them. Try the negative marks calculator.
- Shopping: discounts and tax; the discount calculator handles stacked offers.
- Finance: interest rates, returns and inflation.
- Health: body-fat percentage, nutrition labels, % daily values.
A note on precision
Round only at the end of a calculation. Rounding an intermediate step, such as 33.3% instead of ⅓, can shift the final answer noticeably on large numbers. Our calculator keeps full precision and shows up to six decimal places.
Use the calculator below; every row answers one of the four formulas above.
Try it: Percentage Calculator
Four everyday percentage questions answered instantly — percent of, what percent, percentage change and reverse percentage.