What is a percentage?
A percentage is a fraction with a denominator of 100: 21% is 21/100 = 0.21. So finding X% of something means multiplying by X and dividing by 100. Almost every percentage problem comes down to one of these formulas:
| You want | Formula | Example |
|---|---|---|
| X% of Y | Y · X / 100 | 21% of 80 = 16.8 |
| What % X is of Y | X / Y · 100 | 18 out of 24 = 75% |
| Increase Y by X% | Y · (1 + X/100) | 100 + 20% VAT = 120 |
| Decrease Y by X% | Y · (1 − X/100) | 60 − 15% = 51 |
| Percentage change from A to B | (B − A) / A · 100 | 250 to 310 = +24% |
| Original value before an increase | Final / (1 + X/100) | 120 incl. VAT → 100 before VAT |
The most common mistake: removing tax or a markup by subtracting
If a price including 20% VAT is 120, the price before VAT is not 120 − 20% = 96, but 120 / 1.20 = 100. The 20% was applied to the price before tax, not to the final price. The same happens with stacked discounts: 20% off and then another 20% off is not 40% off, but 1 − 0.8·0.8 = 36% off. Use the "Original value before the %" box to reverse any increase or discount correctly.
VAT, GST and sales tax
The country selector loads the standard VAT or GST rate for each country. Many countries also have reduced rates for food, medicine or books, and rates can change, so check the current one if you need it for something official. In the United States there is no VAT; sales tax depends on the state and city, so type your local rate in the percentage box.
Direct and inverse proportions (rule of three)
In a direct proportion, when one quantity increases the other does too (more kilos, higher price): x = B·C / A. In an inverse proportion, when one increases the other decreases (more workers, fewer days): x = A·B / C.
Example · inverse proportion
3 taps fill a tank in 4.5 hours. How long do 10 taps take? More taps, less time: x = 3 · 4.5 / 10 = 1.35 hours.
Frequently asked questions
What is the difference between percentage points and percent?
If unemployment goes from 10% to 12%, it rises by 2 percentage points, but in relative terms it rises by 20% (2 / 10). They are different things and are often confused in the news.
How do I calculate a percentage increase between two numbers?
Subtract the old value from the new one, divide by the old value and multiply by 100. Use the "Percentage change" box: it also tells you whether it is an increase or a decrease.
How do I work out a weighted grade with percentages?
Multiply each grade by its weight, add them up and divide by 100. The final grade calculator does it for you and tells you what you need on the final exam.