Why a 20% drop needs a 25% gain
A value starts at 100 and falls by 20%. That leaves 80. You need 20 to get back to 100, but the gain is measured from 80. Divide 20 by 80: the return gain is 25%. Adding 20% to 80 would reach only 96.
Enter the loss percentage you already know. The main result, Gain needed to recover, is the increase required from the value left after the drop. This page answers a different question from finding the percentage decrease between two amounts. If you have the starting and ending amounts but not the loss rate, use the Percentage Decrease Calculator first.
How to read the result
Enter the drop as a percentage
Type 20 for a 20% loss. The field is already a percentage, so 0.20 means 0.20%. The default 20% is an example; replace it with the rate you want to examine.
Check what remains
Value left from 100 shows the reduced base. Points lost from 100 shows the gap back to the start. The same percentages work for any positive starting value.
Apply the gain to the reduced value
Gain needed to recover uses the remaining value as its base. It describes a mathematical return to the starting value, not a prediction that the gain will occur.
The recovery formula
Remaining percentage = 100 − Loss percentage
Required gain (%) = Loss percentage ÷ Remaining percentage × 100
The loss percentage measures the amount removed from the original. The required gain measures that same amount against what remains. As the remaining base shrinks, restoring the same number of units takes a larger percentage increase. The calculator keeps the input percentage exact to four decimal places and rounds only the displayed gain to six decimal places.
Check the 20% example by hand
Starting value: 100
After a 20% loss: 100 − 20 = 80
Gap to restore: 100 − 80 = 20
Gain on 80: 20 ÷ 80 × 100 = 25%
Check the answer by increasing 80 by 25%: 80 × 1.25 = 100. The 20 is a difference in points on the reference scale; 25% is the relative gain on the reduced value. A price, production total, or account value that changes only by these percentages follows the same arithmetic.
How the required gain grows with the loss
| Loss | Value left | Gain needed |
|---|---|---|
| 10% | 90 | about 11.111111% |
| 20% | 80 | 25% |
| 50% | 50 | 100% |
| 75% | 25 | 300% |
| 100% | 0 | No finite percentage gain |
A 50% loss halves the value, so the remaining half must double. That is a 100% gain. A 75% loss leaves one quarter, which must quadruple; the increase from one quarter to the whole is 300%. The gain grows sharply as the loss approaches 100%.
Use the same method with an actual amount
The reference value of 100 makes the percentages visible, but the starting amount can be any positive number. Suppose a value falls from 120 to 90. The decrease is 30 out of the original 120, or 25%. Enter 25 as the loss. The calculator shows a gain of about 33.333333% because the 30 needed to get back to 120 is one third of the reduced 90.
For this example, 90 + 30 = 120. The exact gain is 30 ÷ 90 × 100 = 33⅓%. Applying the rounded six-decimal display to 90 may land a tiny amount above or below 120, so use the unrounded fraction when exact equality matters. The result is a percentage on 90; it is not a 33.333333-point change from the original 120.
Combine consecutive drops before using the calculator
If a value falls more than once, first find its overall loss from the original. Two successive 20% drops take 100 to 80, then 80 to 64. The second drop removes 16, so the combined loss is 36%, not 40%. Enter 36 and the required recovery gain is 56.25%: 64 × 1.5625 = 100.
Adding the two stated loss rates would treat both drops as if they used the original 100. This calculator expects one overall loss rate. When you have the original and current amounts, the Percentage Change Calculator can find that overall change first. The recovery answer then applies to the current value, even if several earlier changes led there.
Zero, total loss, and precision
A 0% loss needs a 0% gain. At exactly 100%, the value left is zero. A percentage gain multiplies its current base, so no finite percentage gain from zero can recreate a positive starting value. Putting in new money or adding units is a different operation.
Positive losses below 100% can have repeating decimal recovery gains. For example, a 10% loss needs 10 ÷ 90 × 100 = 11.111111…%. The calculator displays about 11.111111%, rounded to six decimal places and marked with ≈. That displayed figure is an approximation, not a guaranteed minimum that always reaches the start when applied literally. Use the formula when exact equality or a minimum threshold matters. Input accepts up to four decimal places; it rejects percentages above 100 and entries with symbols or commas.
What this comparison leaves out
This is a calculation about the value itself. If you apply it to an investment, a price returning to an earlier price does not by itself establish that your overall return is zero. Income, commissions, other fees, taxes, and the length of time held may matter. FINRA's explanation of return and rate of return distinguishes a gain in value from a full investment return and explains why the base of a percentage matters. FINRA's return example includes income and costs that a simple price comparison omits.
The calculator does not project future gains, account for extra deposits or withdrawals, or model a sequence of several losses and gains. It treats one percentage drop and one possible recovery gain on the reduced value. For an amount before a known decrease, the Reverse Percentage Calculator answers a related but different question.
Frequently asked questions
Why does a 20% loss need a 25% gain?
The loss takes 100 down to 80. Returning from 80 to 100 requires 20 more, and 20 is 25% of 80. The loss and recovery use different starting values.
Is the recovery gain the same as the loss percentage?
Only when the loss is zero. For a positive loss below 100%, the gain must be larger because it is measured against the smaller value left after the loss.
What happens after a 50% loss?
Half the starting value remains. The remaining half must double to reach the original, so the required gain is 100%.
Can a 100% loss be recovered with a percentage gain?
No. A 100% loss leaves zero, and multiplying zero by any finite percentage increase still gives zero. Adding a new amount would be a separate action.
What does a 0% loss show?
The value has not fallen, so the required recovery gain is 0%.
Should I type 20 or 0.20 for a 20% loss?
Type 20. The field takes a percentage number. Typing 0.20 means a loss of 0.20%, which needs a different recovery gain.
Can I add two losses and enter their sum?
Only if both losses were measured from the same original value. Two successive 20% drops take 100 to 80 and then 64. The combined loss is 36%, which needs a 56.25% gain from 64 to return to 100.
Does this include fees, dividends, or time to recover?
No. It compares one value before and after a drop. Investment total return can also depend on income, costs, taxes, and the time period.
Related calculators
- Percentage Decrease Calculator — find the loss rate from a starting and ending amount.
- Percentage Increase Calculator — measure an actual increase between two amounts.
- Reverse Percentage Calculator — find an original amount when you know the later value and change rate.