Why a 20% Increase Then a 20% Decrease Leaves You Down 4%

A 20% increase followed by a 20% decrease does not return you to where you started — it leaves you 4% lower. This single result accounts for a large share of errors in pricing, budgeting, and interpreting statistics, and it happens because percentages are always calculated against a moving base.

The arithmetic is trivial once the frame is set, and you can check any step of it with our percentage change calculator, which keeps the base straight for you.

Why the Round Trip Fails

Start with $100.

1. Increase by 20%: 100 × 1.20 = $120. The base was $100, so the gain was $20.
2. Decrease by 20%: 120 × 0.80 = $96. The base is now $120, so the loss is $24.
3. Net change: −$4, or −4%.

The asymmetry is structural, not a rounding artefact. The same imbalance appears at every magnitude: +50% then −50% leaves you at 75; +10% then −10% leaves you at 99. The loss is always larger than the gain because the decrease is taken from a bigger number.

The Recovery Table

How much do you need to gain back after a drop? More than the drop itself, always:

Drop	Remaining value	Gain required to break even
10%	90.0%	11.1%
20%	80.0%	25.0%
33%	66.7%	50.0%
50%	50.0%	100.0%
75%	25.0%	300.0%

The formula for the break-even gain is d ÷ (1 − d), where d is the drop as a decimal. A 20% drop gives 0.20 ÷ 0.80 = 0.25, or 25%. This is the same relationship behind the well-known fact that a stock falling 50% needs to double to recover.

Where This Bites in Practice

Three everyday situations where the moving base causes real losses:

• Discount then markup. A retailer who discounts a $80 item by 25% to $60, then marks it back up 25%, lands at $75, not $80. The margin lost is permanent unless the markup is recalculated as 33.3% (20 ÷ 60).
• Investment losses. A portfolio down 30% needs a 42.9% gain to break even. This asymmetry is why drawdown control matters more than upside capture over long horizons.
• Inflation and wages. If prices rise 8% and your raise is 8%, you have not kept pace. Your real wage change is 1.08 ÷ 1.08, applied to different bases — and the correct comparison is (1.08 ÷ 1.08 − 1) computed on the same reference point, which requires converting both to index values first.

Percentage Points Are Not Percentages

A rate moving from 4% to 6% has risen by 2 percentage points but by 50% in relative terms. Both statements are correct; they answer different questions. Reporting the wrong one is one of the most common forms of misleading statistics. When you see a headline claiming a “100% increase in risk,” always check whether the underlying figure moved from 1 in a million to 2 in a million — the relative change is real, the practical significance may not be.

Frequently Asked Questions

How do I average a series of percentage changes? You cannot average them arithmetically. A +50% and a −50% year average to 0% arithmetically, but the actual result is −25%. Use the geometric mean: √(1.5 × 0.5) − 1 = −13.4% per year.

Does the order of changes matter? No. Multiplication is commutative, so +20% then −20% gives the same −4% as −20% then +20%. What matters is the base at each step, not the sequence.

How do I reverse a percentage change correctly? Divide rather than subtract. To undo a 25% increase, divide by 1.25; do not subtract 25%. For the full set of percentage operations — increase, decrease, reverse, and difference — see the percentage calculator, or work through any intermediate step with the basic math calculator.