How to Calculate Percentages: 5 Everyday Formulas
Learn the five percentage calculations you need most, from finding a percentage of a number to percentage change, with worked examples and mental math shortcuts.
By Daily Desk Tools · · 2 min read
Percentages show up everywhere: discounts, tips, pay rises, grades and price changes. They all come from one relationship, and once you see it, every percentage question becomes simple.
Part = Percent × Whole ÷ 100
Below are the five versions of that formula you will use most. You can check any of them with our percentage calculator.
1. What is X% of Y?
Multiply the number by the percentage, then divide by 100.
20% of 65 = 65 × 20 ÷ 100 = 13
Mental shortcut: 10% is the number with the decimal point moved one place left. So 10% of 65 is 6.5, and 20% is double that: 13.
2. X is what percent of Y?
Divide the part by the whole, then multiply by 100.
18 out of 24 = 18 ÷ 24 × 100 = 75%
This is how test scores become percentages.
3. Percentage change
Subtract the old value from the new value, divide by the old value, then multiply by 100.
A price rises from 40 to 50: (50 − 40) ÷ 40 × 100 = 25% increase
If the result is negative, it is a decrease. A drop from 50 to 40 is (40 − 50) ÷ 50 × 100 = −20%. Notice the two answers are different, because each change is measured from a different starting value.
4. Increase or decrease by a percentage
To increase, multiply by (1 + percent ÷ 100). To decrease, multiply by (1 − percent ÷ 100).
30% off 80 = 80 × 0.7 = 56
A 5% raise on 42,000 = 42,000 × 1.05 = 44,100
5. Find the original number
If you know a part and what percentage it represents, divide the part by the percentage and multiply by 100.
15 is 25% of what? 15 ÷ 25 × 100 = 60
This is useful for working backwards, such as finding a price before tax when you know the tax amount and rate.
Percent versus percentage points
If a rate goes from 4% to 6%, it has risen by 2 percentage points, but by 50 percent relative to where it started. News reports and financial documents often mix these up, so it is worth checking which one is meant.
Common mistakes
- Reversing changes: a 50% rise followed by a 50% fall does not return you to the start. 100 becomes 150, then 75.
- Adding percentages of different totals: 10% of one bill plus 10% of another is not 20% of either.
- Dividing by the wrong number: for percentage change, always divide by the original value.
When in doubt, write down which number is the part and which is the whole, then use the percentage calculator to check your answer.