Percentage formulas
“Percent” means “per hundred”, so 20% is 20/100 = 0.2. Every calculation above is one of these formulas:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 20% of 150 is 30. |
| X is what % of Y? | X ÷ Y × 100 | 45 is 75% of 60. |
| % change from A to B | (B − A) ÷ |A| × 100 | Going from 80 to 100 is a 25% increase. |
| X is P% of what? | X ÷ (P ÷ 100) | 30 is 20% of 150. |
| Increase Y by P% | Y × (1 + P ÷ 100) | 200 increased by 15% is 230. |
| Decrease Y by P% | Y × (1 − P ÷ 100) | 80 decreased by 25% is 60. |
| % difference | |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 | The percentage difference between 10 and 15 is 40%. |
How to calculate a percentage of a number
Divide the percentage by 100 and multiply by the number. 20% of 150 is 0.20 × 150 = 30. A quick mental shortcut: 10% is the number with the decimal point moved one place left, so 10% of 150 is 15, double it for 20%, halve it for 5%.
| Question | Answer |
|---|---|
| 10% of 50 | 5 |
| 25% of 200 | 50 |
| 15% of 60 | 9 |
| 33% of 300 | 99 |
| 5% of 1,250 | 62.5 |
| 12.5% of 80 | 10 |
Percentage change vs. percentage difference
Percentage change has a direction: it compares a new value to an old one. Going from 80 to 100 is a 25% increase. Going from 250 to 200 is a 20% decrease. Note that a rise and a fall of the same amount aren’t symmetric, going from 100 to 80 is −20%, but from 80 back to 100 is +25%.
Percentage difference compares two values with no “before” and “after”, dividing by their average. Use it to compare two prices, two measurements or two products. The percentage difference between 10 and 15 is 40%.
Don’t confuse either with percentage points. If an interest rate moves from 4% to 5%, it rose by one percentage point, but by 25% in relative terms.
Everyday examples
Tips
On an $80 bill: 15% is $12, 18% is $14.4, 20% is $16, 25% is $20.
Discounts
A 25% discount on $80 leaves you paying 75% of the price: 80 decreased by 25% is 60. Two discounts stack by multiplying, 20% off then 10% off is 0.8 × 0.9 = 0.72 of the price, a 28% total discount, not 30%.
Grades and scores
45 is 75% of 60. That is 45 correct answers out of 60.
Reverse percentages
If $30 is the 20% deposit, the full price is the “of what” question: 30 is 20% of 150.
FAQ
How do I work out 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” row; a negative result means a decrease.
Why is percentage change from 0 undefined?
The formula divides by the starting value. Going from 0 to anything is an infinite relative increase, so the calculator tells you instead of showing a misleading number.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal: adding 15% to 200 is 200 × 1.15 = 230. Use the “Increase” row.
Can I use commas or the % sign?
Yes. 1,250 and 15% are read as 1250 and 15.