Why a 20% Increase Followed by a 20% Decrease Doesn't Cancel Out
October 21, 2026
A 20% increase followed by a 20% decrease does not return you to where you started. It leaves you 4% below. Start with 100, add 20% to get 120, then subtract 20% of 120 (which is 24) to get 96. The second percentage is applied to a bigger number, so it removes more than the first one added.
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Open the Percentage Calculator →The Algebra Behind It
Percentage changes multiply rather than add. An increase of p percent multiplies a value by (1 + p/100), and a decrease of the same size multiplies by (1 − p/100). The product is 1 − (p/100)², which is always less than 1. For 20%: 1 − 0.04 = 0.96. For 10%: 0.99. For 50%: 0.75, so a 50% gain followed by a 50% loss leaves you down 25%.
The bigger the percentages, the bigger the shortfall, which is why the trap matters most for volatile investments.
| Gain then equal loss | Starting at 100 | Net change |
|---|---|---|
| +10% then −10% | 99.00 | −1% |
| +20% then −20% | 96.00 | −4% |
| +50% then −50% | 75.00 | −25% |
| +100% then −100% | 0.00 | −100% |
How to Reverse a Percentage Change
To undo an increase of p percent, you need a decrease of p ÷ (100 + p) as a fraction. To undo a 25% increase, you need a decrease of 25 ÷ 125 = 20%. To undo a 20% decrease, you need an increase of 20 ÷ 80 = 25%.
Check with numbers: 80 plus 25% is 100, and 100 minus 20% is 80. The two percentages are different because they are measured against different bases.
Where This Shows Up in Real Life
Investors see it as the recovery problem: a portfolio that drops 50% needs a 100% gain to return to even. A pay cut of 10% followed by a 10% raise leaves you with 99% of your original pay. Retail prices that are marked up and later discounted by the same percentage end up lower than the original price.
When comparing changes over time, convert to the multiplier form (1.20 and 0.80) and multiply them. It avoids the intuition error and works for any number of steps.
- Use multipliers: +20% is ×1.2, −20% is ×0.8.
- Multiply, do not add, percentage changes in sequence.
- To recover from a loss of p%, you need a gain of p ÷ (100 − p).
Frequently Asked Questions
Why doesn't +20% and −20% equal zero?
The decrease is applied to the larger, post-increase amount. Mathematically, 1.2 × 0.8 = 0.96, a net loss of 4%.
How much do I need to gain to recover from a 30% loss?
You need about a 42.9% gain, since 30 ÷ (100 − 30) = 0.4286.
Is the order of increase and decrease important?
No. Multiplication is commutative, so −20% then +20% also gives 0.96 of the original amount.
How do I average two percentage changes?
Don't just add them. Multiply the multipliers, then take the geometric mean if you want an average rate per period.