Percent Change Formula: Increase and Decrease
Calculate percent increase and decrease with (new − old) / old, and see why going up 25% and back down is not 25%, with two worked examples.
The formula
- % change = (new − old) / old × 100
A positive answer is an increase; a negative answer is a decrease.
The base is always the old value
- Going up: divide by the smaller starting number
- Going down: divide by the larger starting number
Same dollar change, different percent.
Example 1
A price rises from $40 to $50. What is the percent increase?
- Change = 50 − 40 = 10
- Divide by the old value: 10 / 40 = 0.25
25% increase
Example 2
The price then drops from $50 back to $40. What is the percent decrease?
- Change = 40 − 50 = −10
- Divide by the old value (now 50): −10 / 50 = −0.20
20% decrease
Common mistake
Up 25% then down 25% gets you back
The second percent uses a different base.
Always divide by the starting value of that step.
Check: 40 → 50 is +25%, but 50 → 40 is −20%.
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