Percentages appear everywhere: discounts in shops, interest on loans, exam scores, taxes, nutrition labels and statistics in the news. Yet many people still reach for a calculator or guess, because the rules were never explained clearly. This guide shows the three calculations you will use most often, with simple examples and the mistakes to avoid.
What does percent mean?
The word comes from the Latin "per centum", meaning "by the hundred". So 25% means 25 out of every 100, or the fraction 25/100, or the decimal 0.25. Converting between these three forms is the key skill: divide by 100 to turn a percentage into a decimal, and multiply by 100 to go back.
1. Finding X% of a number
Formula: number × percentage ÷ 100
Example: What is 15% of 200? Multiply 200 × 15 = 3,000, then divide by 100 to get 30.
Mental shortcut: to find 10%, move the decimal point one place to the left. For 15%, take 10% and add half of it (20 + 10 = 30 for the number 200).
2. Finding what percent one number is of another
Formula: part ÷ whole × 100
Example: You answered 42 questions correctly out of 60. What is your score? 42 ÷ 60 = 0.7, and 0.7 × 100 = 70%.
3. Percentage increase and decrease
Formula: (new value − old value) ÷ old value × 100
Example (increase): A salary rises from 2,000 to 2,200. The change is 200, and 200 ÷ 2,000 × 100 = 10% increase.
Example (decrease): A product price falls from 80 to 60. The change is −20, and −20 ÷ 80 × 100 = −25%, a 25% decrease.
Applying a percentage change to a price
To increase a number by a percentage, multiply it by (1 + percentage). To decrease it, multiply by (1 − percentage). A 20% increase on 50 is 50 × 1.20 = 60. A 20% discount on 50 is 50 × 0.80 = 40.
Common mistakes to avoid
- Going up and down by the same percentage. If a price rises 50% and then falls 50%, you do not return to the start. 100 becomes 150, and 150 minus 50% is 75. The base changed, so the percentages are not symmetric.
- Confusing percentage points with percent. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points but a 50% increase in the rate itself.
- Adding successive percentages. A 20% discount followed by another 10% is not 30% off. It equals 1 − (0.8 × 0.9) = 28%.
- Using the wrong base. Always divide by the original (old) value when calculating a change, not the new one.
Reverse percentages
Sometimes you know the final price and the percentage but need the original. If a jacket costs 60 after a 25% discount, the original price is 60 ÷ 0.75 = 80. Divide by (1 − discount), not add the discount back.
Where percentages matter in daily life
- Comparing offers: a 30% discount on a 90 item beats 20% off a 100 item (63 vs 80).
- Understanding loans: interest rates are percentages applied over time.
- Reading statistics: "a 50% increase" means little without knowing the starting number.
- Tracking progress: how much of a goal you have completed.
When you want to check an answer or run several calculations quickly, use our Percentage Calculator. It handles all three types in one place and shows the result as you type.