"Percent" means "per hundred," so 25% is 25 out of every 100, or 0.25 as a decimal. Almost every percentage question you'll run into is one of three problems: finding a percent of a number, finding what percent one number is of another, or finding the whole when you know a part and its percent. Add percent change and reverse percentages (like working back from a sale price) and you've covered nearly everything from tips to test scores to pay raises. Each one is below, with a formula and worked examples.
The three core percentage problems
Every basic percentage problem uses the same three quantities: the part, the whole, and the percent. If you know any two, you can find the third.
| You want | Formula | Example |
|---|---|---|
| The part (X% of Y) | part = percent ÷ 100 × whole | 15% of 80 = 0.15 × 80 = 12 |
| The percent (X is what % of Y) | percent = part ÷ whole × 100 | 18 of 24 = 18 ÷ 24 × 100 = 75% |
| The whole (X is Y% of what) | whole = part ÷ (percent ÷ 100) | 30 is 12% of 30 ÷ 0.12 = 250 |
1. How to find a percentage of a number
Convert the percent to a decimal by dividing by 100 (move the decimal point two places left), then multiply.
- 15% of 80: 0.15 × 80 = 12
- 18% tip on a $62.40 bill: 0.18 × 62.40 = $11.23 (11.232, rounded to the cent)
- 7.25% of $250: 0.0725 × 250 = $18.13 (18.125, rounded)
Mental math shortcut: 10% of a number is the number with the decimal point moved one place left, and 1% is two places left. Build other percents from those. For the $62.40 bill, 10% is $6.24, 5% is half that ($3.12), and 1% is about $0.62. So 18% = 10% + 5% + 3 × 1% ≈ 6.24 + 3.12 + 1.87 = $11.23.
The swap trick: X% of Y always equals Y% of X. 8% of 50 is awkward, but 50% of 8 is obviously 4, and both equal 4.
2. How to find what percent one number is of another
Divide the part by the whole, then multiply by 100.
- 18 out of 24: 18 ÷ 24 = 0.75, × 100 = 75%
- A test score of 37 out of 45: 37 ÷ 45 = 0.8222…, × 100 = 82.22%
- 3/8 as a percent: 3 ÷ 8 = 0.375 = 37.5%
The most common mistake is dividing the wrong way round. The "whole" (what you're comparing against) always goes on the bottom. Ask yourself "out of what?" and that number is the divisor. For combining several scores into a course grade, see how to calculate your final grade.
3. How to find the whole from a part and a percent
Divide the part by the percent written as a decimal.
- 30 is 12% of what? 30 ÷ 0.12 = 250
- A $45 deposit is 15% of the total. What's the total? 45 ÷ 0.15 = $300
Check by going forward: 12% of 250 is 30. ✓
The Percentage Calculator has a mode for each problem type, plus percent increase and decrease.
Percentage Calculator →How to calculate percent change (increase or decrease)
Percent change measures how much something grew or shrank relative to where it started:
percent change = (new − old) ÷ old × 100
A positive result is an increase; a negative result is a decrease.
| Change | Calculation | Result |
|---|---|---|
| 40 → 52 | (52 − 40) ÷ 40 × 100 | +30% |
| 52 → 40 | (40 − 52) ÷ 52 × 100 | −23.08% |
| Salary $58,000 → $61,770 | (61,770 − 58,000) ÷ 58,000 × 100 | +6.5% |
| 1,250 → 1,100 visitors | (1,100 − 1,250) ÷ 1,250 × 100 | −12% |
Look at the first two rows. Going from 40 to 52 is a 30% increase, but going from 52 back to 40 is only a 23.08% decrease. The change is the same 12 units both times, but it's divided by a different starting value. Always divide by the old value.
If the numbers you're comparing are themselves percentages, like an interest rate going from 5% to 6%, there are two valid answers: a 1 percentage point rise, or a 20% increase. Percentage vs. percentage points explains when to use each.
Adding or subtracting a percentage
To increase a number by a percent, multiply by (1 + percent). To decrease it, multiply by (1 − percent). This gets the answer in one step.
- 45 plus 8%: 45 × 1.08 = 48.60
- $60 minus 25%: 60 × 0.75 = $45
Reverse percentages: finding the original value
Reverse percentage problems give you the value after a percentage change and ask for the value before. The fix is to divide by the same multiplier you'd have used going forward. Don't apply the percentage to the new number.
Original price before a discount
A jacket costs $64.80 after a 20% discount. What was the original price?
- Right: the sale price is 80% of the original, so original = 64.80 ÷ 0.80 = $81.00.
- Wrong: adding 20% back gives 64.80 × 1.20 = $77.76. That's too low, because the 20% discount was taken from the larger original price, not from $64.80.
Price before sales tax
A receipt shows $107.25 including 7.25% sales tax. What was the pre-tax price?
- Right: 107.25 ÷ 1.0725 = $100.00.
- Wrong: subtracting 7.25% of the total gives 107.25 × 0.9275 = $99.47, which is 53 cents off.
Check either answer by going forward: $81.00 × 0.80 = $64.80, and $100.00 × 1.0725 = $107.25. ✓
Percentages that stack
When percentages apply one after another, multiply the multipliers. Don't add the percents.
- 30% off, then an extra 20% off: 0.70 × 0.80 = 0.56, so you pay 56% of the original price. That's a 44% total discount, not 50%.
- Up 20%, then down 20%: 1.20 × 0.80 = 0.96. You end 4% below where you started, not back at the original.
Converting between percents, decimals and fractions
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/8 | 0.375 | 37.5% |
| 1/5 | 0.2 | 20% |
| 1/3 | 0.333… | 33.33% |
| 9/200 | 0.045 | 4.5% |
To go from a decimal to a percent, multiply by 100 (0.045 → 4.5%). To go from a percent to a decimal, divide by 100 (4.5% → 0.045).
Quick reference
- X% of Y: X ÷ 100 × Y
- X is what % of Y: X ÷ Y × 100
- X is Y% of what: X ÷ (Y ÷ 100)
- Percent change: (new − old) ÷ old × 100
- Original before a change: new ÷ (1 ± percent as a decimal)
Percentages also show up in exchange-rate fees and markups. How currency conversion works walks through one common example.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percent by 100 and multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 18 out of 24 is 18 ÷ 24 × 100 = 75%.
How do I calculate percent increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Going from 40 to 52 is (52 − 40) ÷ 40 × 100 = a 30% increase.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount as a decimal. A $64.80 price after 20% off was originally 64.80 ÷ 0.80 = $81.00. Adding 20% to the sale price gives the wrong answer.
Is X% of Y the same as Y% of X?
Yes. Multiplication works in either order, so 8% of 50 and 50% of 8 both equal 4. Swapping can make mental math much easier.