Percentages show up everywhere money does: tips, sales, raises, tax, interest and price changes. The good news is that almost every problem is one of a few patterns. Learn the patterns and you can do most of them on a phone calculator in seconds.
The short version
- “Percent” means “out of 100”. 25% = 25 ÷ 100 = 0.25.
- To find X% of a number, multiply by X ÷ 100.
- Percent change = (new − old) ÷ old × 100.
- To work backward from a price after a change, divide; don’t subtract the percentage.
1. What is X% of a number?
Turn the percentage into a decimal (divide by 100) and multiply.
Example
20% of $85: 85 × 0.20 = $17. That’s the tip on an $85 restaurant bill.
Shortcut: 10% is the number with the decimal point moved one place left ($8.50). Double it for 20% ($17). Half of 10% is 5% ($4.25).
2. What percent is one number of another?
Divide the part by the whole and multiply by 100.
Example
You’ve saved $450 toward a $1,800 goal: 450 ÷ 1,800 × 100 = 25%.
3. Percent increase or decrease
Subtract the old value from the new one, divide by the old value, multiply by 100. A negative answer is a decrease.
Example
A gallon of milk averaged $4.17 in August 2025 and $4.23 in August 2026 (BLS). (4.23 − 4.17) ÷ 4.17 × 100 = about 1.4% higher. Eggs went from $3.59 to $2.27: (2.27 − 3.59) ÷ 3.59 × 100 = about −36.8%.
Always divide by the starting value. Dividing by the new value is the most common mistake, and it gives a different answer.
4. Add a percentage (tax, tip, raise)
Multiply by 1 plus the percentage as a decimal.
Example
A $60 item with 6.5% sales tax: 60 × 1.065 = $63.90. A $52,000 salary with a 3% raise: 52,000 × 1.03 = $53,560.
5. Take a percentage off (discounts)
Multiply by 1 minus the percentage as a decimal.
Example
A $120 jacket at 25% off: 120 × 0.75 = $90. You save $30.
Two discounts don’t add up. “20% off, then an extra 10% off” is 0.80 × 0.90 = 0.72, which is 28% off, not 30%. Our guide on calculating discounts has more examples.
6. Work backward to the original number
If you know the price after a change, divide by the same factor you would have multiplied by.
Example
A shirt costs $64 after 20% off. The original price was 64 ÷ 0.80 = $80. A receipt shows $53.25 including 6.5% tax, so the pre-tax price was 53.25 ÷ 1.065 = $50.
This is why “add 20%, then take 20% off” doesn’t return you to the start: 100 × 1.20 × 0.80 = 96.
7. Percent vs. percentage points
When a rate moves from 6% to 7.5%, it rose by 1.5 percentage points, but by 25 percent (1.5 ÷ 6 × 100). News stories about interest rates and tax rates usually mean percentage points. Ask which one is meant before comparing.
Quick reference
| You want to… | Formula | Example |
|---|---|---|
| Find X% of N | N × X ÷ 100 | 15% of 240 = 36 |
| Find what % A is of B | A ÷ B × 100 | 30 of 120 = 25% |
| Percent change | (New − Old) ÷ Old × 100 | 50 → 60 = +20% |
| Add X% | N × (1 + X ÷ 100) | 80 + 5% = 84 |
| Subtract X% | N × (1 − X ÷ 100) | 80 − 5% = 76 |
| Original before a change | Result ÷ (1 ± X ÷ 100) | 76 after 5% off ← 80 |
Our free percentage calculator does all of these, and you can type questions like “15% of 240” into our Quick Answers box.
The short version
Convert the percentage to a decimal, then multiply for “of”, add 1 for increases, subtract from 1 for discounts, and divide to work backward. With those four moves, almost any everyday percentage problem takes one line.
More everyday uses
- Test scores: 42 correct out of 50 is 42 ÷ 50 × 100 = 84%.
- Budget shares: $1,450 rent out of $3,860 take-home pay is 1,450 ÷ 3,860 × 100 ≈ 37.6% of income.
- Savings rate: saving $300 of a $4,000 paycheck is 7.5%.
- Monthly interest: a credit card APR of 24% is roughly 24 ÷ 12 = 2% a month on the balance.
- Commission: a 6% commission on a $12,500 sale is $750.
Common mistakes to avoid
- Dividing by the wrong number in percent change. Always divide by the starting value.
- Adding percentages that apply one after another. A 10% raise followed by a 10% raise is 21% total, not 20% (1.10 × 1.10 = 1.21).
- Subtracting to undo a percentage. To remove 8% tax from a total, divide by 1.08; don’t take 8% off.
- Mixing up percent and percentage points when comparing rates.
Doing it without a calculator
Break the percentage into easy pieces: 10%, 5% and 1%. For 17% of $240: 10% is $24, 5% is $12, 1% is $2.40, and 1% again is $2.40. Add 24 + 12 + 2.40 + 2.40 = $40.80. With practice, most everyday percentages take a few seconds this way.
Another handy trick: X% of Y equals Y% of X. So 8% of 50 is the same as 50% of 8, which is 4.
