Percentages turn up everywhere — discounts, tips, interest rates, test scores, statistics. The good news is that every percentage problem comes down to one idea and a little arithmetic. This guide walks through the three questions that cover almost every real-world case, with worked examples you can follow by hand.
What is a percentage?
A percentage is a way of writing a number as a fraction of 100. The word comes from the Latin per centum — "per hundred". So 25% means 25 out of every 100, which is the fraction 25/100, which is the decimal 0.25. That single fact — percent means "divide by 100" — is the key to everything below.
Because a percentage is just a scaled fraction, converting a percent to a decimal (divide by 100) or back (multiply by 100) is usually the first or last step of any percentage calculation.
The three percentage questions
Almost every percentage problem is one of these three. Learn the pattern for each and you're set.
1. What is X% of Y?
Convert the percent to a decimal and multiply by the number. For example, 20% of 80 is (20 ÷ 100) × 80 = 0.2 × 80 = 16. A 15% tip on a $60 bill is 0.15 × 60 = $9.
2. X is what percent of Y?
Divide the part by the whole, then multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%. If you scored 18 out of 20 on a quiz, that's (18 ÷ 20) × 100 = 90%.
3. What is the percentage change from X to Y?
Take the difference, divide by the original value, then multiply by 100. Going from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%. A positive answer is an increase; a negative answer is a decrease. The original value is always the base you divide by — that detail matters more than people expect.
Percentages, decimals, and fractions
Switching between these three forms makes mental math much easier. Here are the conversions worth memorizing:
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 25% | 0.25 | 1/4 |
| 33.3% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
Need to go the other way? See our guide on converting fractions to decimals or use the Fraction to Decimal Converter.
Mental math shortcuts
- 1% of a number is the number ÷ 100 (move the decimal two places left).
- 10% is the number ÷ 10 (move the decimal one place left).
- 5% is half of 10%.
- 20% is double 10%; 15% is 10% plus half of 10%.
- 50% is just half; 25% is half of that again.
Common mistakes to avoid
- Forgetting to divide by 100 — "20% of 80" is 16, not 1,600.
- Using the wrong base for percentage change — always divide by the starting value.
- Assuming a percentage increase and the same percentage decrease cancel out. They don't — see Percentage Increase vs Decrease.
- Rounding too early. Keep full precision until the final step, then round.