To recover an investment loss of L%, the required gain is L ÷ (100 − L) × 100%. A 20% loss requires a 25% gain, while a 50% loss requires a 100% gain. The examples below apply this calculation to Bitcoin prices and exclude trading fees.
Here, L is the loss expressed as a percentage, such as 20 for a 20% loss. The formula applies when 0 ≤ L < 100. A 100% loss leaves a zero balance, so no finite percentage gain on that remaining balance restores the original amount.
Replacing lost coins or recovering stolen funds is a different problem. This page calculates the price increase needed to return to the starting value after a percentage loss.
How to calculate the gain needed to recover a loss
Let the loss percentage be L, expressed as a number between 0 and 100. The gain needed to return to the original value is L / (100 − L) × 100%.
For a 20% loss, the calculation is 20 / 80 × 100% = 25%. For a 50% loss, it is 50 / 50 × 100% = 100%.
You can also work directly from prices: required gain = (original price / current price − 1) × 100%.
The formula assumes a positive current value and an unchanged asset quantity. It excludes fees, interest and any purchases or sales during the period.
Loss percentage and gain needed to break even
Each example starts from a hypothetical value of $100:
| Loss | Remaining from 0 | Gain needed to recover |
|---|---|---|
| 10% | 11.11% | |
| 20% | 25.00% | |
| 30% | 42.86% | |
| 40% | 66.67% | |
| 50% | 100.00% | |
| 60% | 150.00% | |
| 80% | 400.00% | |
| 90% | 900.00% |
The dollar gap is measured against the original value when calculating the loss and against the remaining value when calculating the recovery. Mixing those denominators creates the apparent contradiction.
For a check using two prices, open our Bitcoin percentage-change calculator. Enter the lower value as the starting price and the original value as the ending price to measure the required recovery.
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Why a 20% drop followed by a 20% rise still leaves a loss
Start with $100. A 20% decline leaves $80. A subsequent 20% rise adds $16, bringing the value to $96.
The net change is −4%, not zero. Calculate it by multiplying the growth factors: 0.80 × 1.20 − 1 = −0.04.
For an equal fall and rise of d expressed as a decimal, the combined change is (1 − d) × (1 + d) − 1 = −d². The order of those two factors does not change that result.
This is why adding consecutive percentage moves can give the wrong answer. Each move uses the value at the beginning of its own interval.
A hypothetical Bitcoin price example
Suppose Bitcoin falls from $60,000 to $42,000. The decline is ($42,000 − $60,000) / $60,000 = −30%.
To return from $42,000 to $60,000, the required gain is ($60,000 − $42,000) / $42,000, or approximately 42.86%.
For a fixed holding of 0.01 BTC, the corresponding value falls from $600 to $420. The price-recovery percentage is the same. These are illustrative prices, not current market data.
Price recovery and personal break-even are different
Returning to an earlier chart price does not necessarily restore your account's original cash balance. Fees or changes in the quantity you hold can change your personal break-even point.
An earlier market high is also not automatically your purchase price. If you entered after the decline began, use your own entry price and cost records when calculating your position's result.
Our percentage-change guide explains how to choose the starting value for a price comparison.
Can this formula measure leveraged account losses?
It can describe the percentage increase from one positive account value to another, but it does not turn an asset's price recovery into a leveraged account recovery. Liquidation, financing charges and position changes can break that connection.
Use the loss-to-recovery formula for the specific quantity you are measuring. State whether you mean the asset price, a fixed holding or an account balance.
What happens after a 100% loss?
The formula has a zero denominator at a 100% loss. No finite percentage gain from a value of zero restores a positive starting value. That mathematical limit is another reason not to describe losses and gains as interchangeable percentages.
To compare a decline with its recovery, keep the starting value visible, use the correct denominator and check your calculation before drawing a conclusion about a trade.
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