What This Calculator Does
When an investment, account balance, or any quantity drops by a certain percentage, you need a larger percentage gain to climb back to where you started. This is because the gain is applied to a smaller base. This calculator tells you exactly what percent increase is required to fully recover from any percentage loss.
How to Use It
Enter the percentage you lost (for example, 20 for a 20% drop) and press calculate. The tool shows the required percent gain to break even, along with the recovery multiplier — the factor your reduced value must be multiplied by to return to the original.
The Formula Explained
The required gain is given by:
$$\text{gain\%} = \frac{\text{loss\%}}{100 - \text{loss\%}} \times 100$$
If you lose L percent, you keep (100 − L) percent of the original value. To get from that smaller base back to 100, you must gain L relative to (100 − L), which is always more than L itself. The bigger the loss, the more dramatically the required gain grows — a 50% loss needs a 100% gain, and a 90% loss needs a 900% gain.
Worked Example
Suppose a stock falls 20%. Plugging in: $$\text{gain\%} = \frac{20}{100 - 20} \times 100 = \frac{20}{80} \times 100 = 25\%.$$ So after a 20% loss you need a 25% gain just to break even. The recovery multiplier is \(100 / 80 = 1.25\times\).
FAQ
Why isn't the recovery gain the same as the loss? Because percentages are relative to the current value. After a loss your base is smaller, so the same dollar recovery represents a bigger percentage of that smaller base.
What happens at a 100% loss? A 100% loss means the value is zero, so no finite percentage gain can recover it. The calculator limits inputs below 100%.
Does this work for any quantity? Yes — it applies to investments, prices, weights, populations, or any value that drops by a percentage and needs to return to its original level.
