Why a 50% Loss Needs a 100% Gain to Break Even
If a $100 investment falls 50%, it is worth $50. A 50% gain on that $50 only brings it back to $75. To get back to $100, it has to double, which is a 100% gain. This lopsided math catches out investors, shoppers, and anyone reading sales reports.
The base keeps moving
Every percent change is measured against the number you start from. After a drop, you are starting from a smaller base, so the same dollar gap is a bigger share of it. Going from $100 to $50 is $50 off a base of $100, which is 50%. Coming back from $50 to $100 is $50 on a base of $50, which is 100%.
Recovery table
| Loss | Gain needed to break even |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 33.33% | 50% |
| 50% | 100% |
| 75% | 300% |
| 90% | 900% |
The formula behind the table is: gain needed = loss ÷ (1 − loss). For a 20% loss, 0.20 ÷ 0.80 = 0.25, or 25%.
Where this shows up in real life
Prices. A store that cuts a $200 coat by 25% to $150 has to raise it 33.33%, not 25%, to get back to $200.
Pay. A 10% pay cut followed by a 10% raise leaves you 1% behind. $1,000 becomes $900, and $900 plus 10% is $990.
Business numbers. If monthly sales fall from 4,000 to 3,000 units, that is a 25% drop. A report saying sales are "up 25%" the next month would only bring them to 3,750.
Check your own numbers
Enter the before and after values in the percent change calculator to see the true change in either direction. If you know the final value and the percent, the reverse percentage calculator recovers the starting number.
Try it with your own numbers.
Open the percent change calculator