Why Does a 50% Drop Need a 100% Gain to Get Back to the Starting Price?

After a 50% drop you need a 100% gain because the percentages are calculated from different bases. If $100 becomes $50, a 50% gain on $50 only gets you to $75. To get back to $100 you need another $50 — that is, 100% of the new, smaller amount. The deeper the drop, the faster the required gain grows: after −80% you need +400%.

How do you calculate it yourself?#

The required gain after an X% drop is:

required gain = X / (100 − X) × 100%

Example: a 30% drop. 30 / 70 × 100% ≈ 42.9%. Check: $100 × 0.7 = $70, and $70 × 1.429 ≈ $100.

Small drawdowns recover almost one-for-one. Deep ones require gains of several times.

What does this look like for Bitcoin?#

• Bitcoin's all-time high is $126,198, set on October 6, 2025, according to CoinLaw.
• In early February 2026 the price fell to roughly $60,000, Yahoo Finance reports. That is a drop of about 52.5%, and recovering from there required a gain of about 110%.
• On September 23, 2026 Bitcoin traded near $86,140, per CoinDesk. That is still about 31.7% below the high, which is roughly +46.5% away.

Meanwhile the price has already risen about 43.6% from the February low. A large percentage gain does not mean losses have been recovered: it all depends on the starting point.

Why don't equal percentage gains and losses cancel out?#

Because the second percentage applies to an amount that has already changed:

• $100 → +10% → $110 → −10% → $99. Result: −1%.
• $100 → +50% → $150 → −50% → $75. Result: −25%.

Order does not matter: −50% then +50% also leaves $75. The bigger the swings, the stronger the effect. That is why averaging percentages misleads: +50% and −50% average to 0%, but the real result is a loss of a quarter.

What does this mean for beginners?#

1. Look at amounts, not just percentages. "Up 40%" and "back to my purchase price" are different statements.
2. Measure from your own entry price. The same market move produces different results for someone who bought at the peak and someone who bought after the drop.
3. Account for volatility. Crypto assets often fall by tens of percent; for memecoins, 80–90% drawdowns are not unusual.
4. Remember leverage. With leverage, a drop of a few percent can wipe out a position entirely, leaving nothing to recover.

For why holding many tokens does not always reduce risk, see Why Many Tokens Don't Always Mean Diversification.

What are the limitations of this maths?#

• It does not forecast. The formula shows only the distance to recover, not the probability of covering it.
• Fees are excluded. Every trade costs money, so the real recovery threshold is higher.
• Inflation and currency are excluded. Dollar prices ignore changes in purchasing power and your own currency's exchange rate.
• Prices vary by source. Highs and lows differ slightly across exchanges and aggregators, so the figures are rounded.