Loss Recovery Calculator
The gain you need to get back to even after a loss of any size.
The climb back from a fall
Gain needed after a fall
| Fall | Gain needed | Value left of 100 |
|---|---|---|
| 5.00% | 5.26% | 95 |
| 10.00% | 11.11% | 90 |
| 15.00% | 17.65% | 85 |
| 20.00% | 25.00% | 80 |
| 25.00% | 33.33% | 75 |
| 30.00% | 42.86% | 70 |
| 35.00% | 53.85% | 65 |
| 40.00% | 66.67% | 60 |
| 45.00% | 81.82% | 55 |
| 50.00% | 100.00% | 50 |
| 55.00% | 122.22% | 45 |
| 60.00% | 150.00% | 40 |
| 65.00% | 185.71% | 35 |
| 70.00% | 233.33% | 30 |
| 75.00% | 300.00% | 25 |
| 80.00% | 400.00% | 20 |
| 85.00% | 566.67% | 15 |
| 90.00% | 900.00% | 10 |
How this was calculated
A recovery gain says how much, not how long or whether: it uses no returns, past or future.
For education only, not investment advice: no tool here tells you what to buy, sell or hold. Results use only the figures you enter, the files you load (read in your browser, never uploaded) and the published rules each page names. Check them against your broker's or exchange's own figures, and consider a licensed or registered adviser for advice on your situation.
About the Loss Recovery Calculator
A fall and the rise that undoes it are not the same size. After a 20% loss an account needs a 25% gain to get back to where it started, after a 50% loss it needs 100%, and after a 90% loss it needs 900%. This calculator works out that recovery gain from a loss in percent, or from the value before and after the fall, and the reverse: the loss that a given gain undoes.
The arithmetic is the same for a trading account, a portfolio, a fund or a single share in any currency, so there is nothing to set up. A ready table lists the recovery gain for every fall from 5% to 90%, and the chart shows why deep drawdowns are so hard to climb out of: the curve rises ever faster as the loss grows.
How to use it
- Choose what you know: the loss in percent, the value before and after the fall, or a gain whose matching loss you want.
- Type the numbers. Values can be in any currency and use your usual thousands and decimal separators.
- Read the gain needed (or the loss undone) at the top, with the working below it.
- Use the table and the chart to compare falls of different sizes.
Examples
Gain needed: 25.00%
0.20 ÷ (1 − 0.20) = 0.25: 80 grows back to 100 with a 25% gain.
A 30.00% loss · gain needed 42.86%
100,000 ÷ 70,000 − 1 = 0.4286.
Gain needed: 100.00%
Half of the value has to double to get back to the start.
A 20.00% loss
0.25 ÷ (1 + 0.25) = 0.20.
The formulas
With the loss L and the gain G as fractions (a 20% fall is 0.20):
G = L ÷ (1 − L)
From the value before the fall V₀ and after it V₁:
G = V₀ ÷ V₁ − 1
The reverse, the loss a gain undoes:
L = G ÷ (1 + G)
They all come from the same fact: after a fall of L the value is (1 − L) of what it was, and multiplying by (1 + G) has to bring it back to 1.
Reading the results
- The gain needed is the total rise, in one go or over many periods: a 25% recovery can be two rises of about 11.8% each, because gains compound.
- The deeper the fall, the steeper the climb: up to about 10% the recovery gain is only a little bigger than the loss, after 50% it is twice the loss, and after 80% it is five times the loss.
- Losing everything (100%) cannot be undone by growth: there is nothing left to grow. On leveraged products a loss can exceed 100%, which leaves a debt instead.
What it leaves out
- Money added or withdrawn. New deposits shorten the climb; withdrawals lengthen it. The formula assumes the same money throughout.
- Costs and taxes. Fees, spreads and tax on later gains mean the gross gain has to be a little higher than the figure shown.
- Time. It says how much, not how long: the time a recovery takes depends on returns nobody can know in advance.
Limitations
- It assumes no money is added or taken out during the recovery.
- Costs, taxes and inflation are not included.
- It cannot say how long a recovery will take, or whether it will happen.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
Why does a 50% loss need a 100% gain?
Because the gain is measured on the smaller amount that is left. 100 falls by half to 50; to get back to 100, that 50 has to grow by 50, which is 100% of 50.
How do I work out the gain needed in a spreadsheet?
With the loss as a decimal in A2 (0.3 for 30%), type =A2/(1-A2) and format it as a percentage; from values, use =start/end-1. The reverse is =G/(1+G).
Is the gain needed the same for a share and for a whole portfolio?
Yes. The arithmetic depends only on the size of the fall, so it is the same for one share, a fund, an account or any value in any currency.
What does a loss above 100% mean?
Only leveraged products, such as futures, CFDs or a margin account, can lose more than what was put in. The account is then below zero: growth alone cannot bring it back, it first needs new money to cover the debt.
Does a recovery have to happen in one rise?
No. The gain needed is the total; it can come in many smaller rises that compound. Two rises of about 11.8% each make the 25% that undoes a 20% fall.
How does this relate to drawdowns and position sizing?
A drawdown is the fall from a peak; the recovery gain says how hard it is to climb back. That is one reason traders limit the risk per trade: see the Position Size Calculator.