Loss Recovery Calculator

The loss recovery calculator computes the percentage gain required on a reduced balance to return that balance to its original starting level.

Inputs: Loss percentage (%), Amount — starting balance (your currency, optional), Monthly return (%, optional).

Default preview (30% loss on $10,000.00): Gain needed to recover = 42.86%, Balance after loss = $7,000.00, Amount needed to get back = $3,000.00.

Educational tool. Results are simple calculations based only on the numbers you enter. They are not predictions and not financial advice.

How it works

When an account drops by a percentage, any future percentage gain is multiplied against the smaller remaining balance rather than the original balance. Because the base is smaller, the percentage gain needed to return to the original value is always larger than the percentage loss whenever the loss is above 0% and below 100%. Dividing 1 by the remaining fraction (1 minus the loss decimal) and subtracting 1 produces the break-even gain percentage. If you also enter a starting balance, multiplying it by the remaining fraction gives the balance after the loss, and subtracting that balance from the starting amount gives the shortfall amount needed in your currency to break even. If you enter an assumed constant monthly return above 0%, taking the ratio of the natural logarithm of the recovery factor to the natural logarithm of 1 plus the monthly rate gives the number of compounding months needed to reach the starting balance.

l = L / 100

Gain needed (%) = (1 / (1 - l) - 1) * 100

Balance after loss = B * (1 - l)

Amount needed = B - Balance after loss

Months to recover = ln(1 / (1 - l)) / ln(1 + r / 100)

Worked example

Suppose a balance of $10,000.00 experiences a 30% loss (l = 0.30). Multiplying $10,000.00 by (1 - 0.30) = 0.70 leaves a balance after loss of $7,000.00, creating a shortfall of $3,000.00. Dividing 1 by 0.70 and subtracting 1 gives a gain needed of 42.86% (unrounded: 42.8571%) to bring $7,000.00 back up to $10,000.00. At an assumed constant monthly return of 1% (if every month earned exactly 1% — an assumption, not a forecast), ln(1 / 0.70) / ln(1.01) equals 35.8 months.

How to use the result

Use the gain needed percentage to see how far a reduced balance must rise, in percentage terms, to return to its starting amount. Compare the amount needed in your currency with your balance after the loss to separate the monetary recovery from the percentage change. If you include an assumed monthly return, treat the month count strictly as the arithmetic consequence of earning that exact rate every month with no compounding interruptions.

Frequently asked questions

Why is the percentage gain needed to recover larger than the loss percentage?

A loss shrinks the base that future returns multiply against. Because 1 / (1 - l) - 1 grows faster than l as l increases from 0 toward 1, each additional percentage point of loss leaves a smaller denominator and requires a disproportionately larger percentage gain to reach the original value.

What happens at a 0% loss?

At a 0% loss, l equals 0, so 1 / (1 - 0) - 1 equals 0. The remaining balance equals the full starting amount, the amount needed is 0 in your currency, and the gain needed is 0.00%.

Why can't a 100% loss be recovered with a percentage gain?

When the loss is 100%, l equals 1, so (1 - l) equals 0 and the remaining balance is 0 in your currency. Multiplying 0 by any finite percentage gain still equals 0, and division by zero in 1 / (1 - l) is undefined.

What does the months-to-recover output represent?

Months to recover equals ln(1 / (1 - l)) / ln(1 + r / 100). It is the exact number of months needed if every single month earned exactly r% (an assumption, not a forecast).

Does the starting balance change the required gain percentage?

No. In the formula (1 / (1 - l) - 1) * 100, the percentage gain needed depends only on the loss percentage L. Entering a starting balance calculates the remaining balance after the loss and the amount needed in your currency to get back to that starting balance.

Want to practice these ideas without risking money? EquiTrek is an iOS app with a paper-trading simulator.