After a Loss, How Much Must the Price Rise to Break Even?

Short answer: Required gain = drop ÷ (1 − drop). After a 40% drop you hold 60%, so you need 40% ÷ 60% ≈ 66.67% to get back to the original price.

Why a drop and a recovery are not symmetric

A drop is measured against the original price; a recovery is measured against what is left. The smaller denominator makes the required percentage larger.

A 40% drop turns 100 into 60. Going from 60 back to 100 means adding 40, which is 40 ÷ 60 ≈ 66.67%.

Formulas

Remaining ratio1 − drop
Required gaindrop ÷ (1 − drop)
Equivalent form1 ÷ (1 − drop) − 1

Worked example (recompute it yourself)

Capital 10,000 USDT, price falls 40%:

Remaining value = 10,000 × 0.60 = 6,000 USDT. Recovering means going from 6,000 back to 10,000, a gain of 4,000 ÷ 6,000 = 66.67%.

Cross-check with the formula: 0.40 ÷ 0.60 = 66.67%, matching the step-by-step result.

Drop levels compared

DropRemainingRequired gain
−10%90%+11.11%
−20%80%+25.00%
−25%75%+33.33%
−40%60%+66.67%
−50%50%+100.00%
−60%40%+150.00%
−75%25%+300.00%
−90%10%+900.00%

Pure ratio conversion, excluding fees and slippage.

Adding fees to the recovery line

The figures above are the cost-free recovery line. With a 0.1% fee on both the buy and the sell, the gain needed just to get back to flat is slightly higher.

The formula becomes 1 ÷ [(1 − drop) × (1 − fee)²] − 1. For a 40% drop at a 0.1% fee, this is about 67.00% — roughly 0.33 percentage points above 66.67%.

Notes

The required gain describes only the ratio between two prices. It is independent of the asset and of the price level.

It says nothing about whether such a move will happen. This page makes no market call and offers no buy/sell advice.

If your goal is a specific profit rather than break-even, use the target price calculation instead.

FAQ

Why does a 50% drop require a 100% rise?

100 falling 50% leaves 50. Going from 50 back to 100 needs +50, which is +100% of 50. Halving the base doubles the required gain.

Why does a 90% drop require +900%?

The remaining 10% must grow back to 100%, which means adding 90 points: 90 ÷ 10 = 900%. The deeper the drop, the more disproportionate the gain.

How much does a fee raise the recovery line?

At 0.1% on both sides the example moves from 66.67% to about 67.00%, roughly 0.33 percentage points. Higher rates raise it further.