Percent change calculator
Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease. Enter two numbers to see the change, its direction and the formula.
Which one do you need?
- Percent changeSomething moved from an old value to a new one, like a price, a paycheck or a score. Divide the change by the old value: (new − old) ÷ old × 100. A positive answer is an increase, a negative one a decrease.
- Percent differenceTwo values side by side with no before and after, like two stores' prices. Divide the gap by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. Swapping the two numbers gives the same answer.
- Before a changeYou know the value after a raise or a markdown and want the starting point. Divide by 1 plus the percent (or 1 minus it for a decrease): 120 ÷ 1.2 = 100.
A common slip: to undo a 20% increase, you can't take 20% off the new value. 120 minus 20% is 96, not 100, because the 20% is now taken from a bigger number. That is also why a rise and a fall of the same percent don't cancel out.
When the old value is negative, the change is measured against its size (its absolute value), so going from −40 to −10 counts as an increase.
The change that undoes a change
Start at 100, apply the change, then see what percent brings you back. Rounded to two decimal places.
| Change | Undo it with | Example |
|---|---|---|
| +10% | −9.09% | 100 → 110 → 100 |
| −10% | +11.11% | 100 → 90 → 100 |
| +20% | −16.67% | 100 → 120 → 100 |
| −20% | +25% | 100 → 80 → 100 |
| +25% | −20% | 100 → 125 → 100 |
| −25% | +33.33% | 100 → 75 → 100 |
| +50% | −33.33% | 100 → 150 → 100 |
| −50% | +100% | 100 → 50 → 100 |
Worked examples
What is the percent change from 1,200 to 1,500?
Going from 1,200 to 1,500 is a 25% increase (a change of +300).
(1,500 − 1,200) ÷ 1,200 × 100 = +25%
What is the percent change from 1,500 to 1,200?
Going from 1,500 to 1,200 is a 20% decrease (a change of −300).
(1,200 − 1,500) ÷ 1,500 × 100 = −20%
What is the percent change from −40 to −10?
Going from −40 to −10 is a 75% increase (a change of +30).
((−10) − (−40)) ÷ |−40| × 100 = +75%
What is the percent difference between 40 and 50?
The percent difference between 40 and 50 is about 22.22%.
|40 − 50| ÷ ((40 + 50) ÷ 2) × 100 ≈ 22.22%
66 is 10% more than what number?
If 66 is the value after a 10% increase, the original value was 60.
66 ÷ (1 + 10 ÷ 100) = 66 ÷ 1.1 = 60
Check: 60 + 10% of 60 = 6645 is 25% less than what number?
If 45 is the value after a 25% decrease, the original value was 60.
45 ÷ (1 − 25 ÷ 100) = 45 ÷ 0.75 = 60
Check: 60 − 25% of 60 = 45
Questions
- What is the difference between percent change and percent difference?
- Percent change has a direction: it measures from an old value to a new one, so 40 to 50 is a 25% increase while 50 to 40 is a 20% decrease. Percent difference compares two values without a starting point and divides by their average, so 40 and 50 are about 22.22% apart either way.
- How do I find the original price before a 20% increase?
- Divide the new price by 1.2. A price that is $120 after a 20% increase was $120 ÷ 1.2 = $100 before it.
- Why doesn't a 50% drop followed by a 50% rise get me back?
- The rise is taken from a smaller number. 100 drops 50% to 50, and 50% of 50 is only 25, so you end at 75. Getting from 50 back to 100 takes a 100% increase.
- Can percent change be more than 100%?
- Yes, for an increase. Going from 20 to 50 is a 150% increase. A decrease stops at 100%, which means the value fell to 0.