The Percentage Mistake Almost Everyone Makes
Published 2026-09-14
A simple example that trips people up
Imagine a stock price rises 50%, then falls 50%. Most people's gut instinct is that it ends up back where it started — but it doesn't. Start at $100: a 50% increase brings it to $150. A 50% decrease from $150 is $75, not $100. The stock ends up 25% below where it began, even though the percentages "cancel out" on paper.
Why this happens
The core issue is that percentage increases and decreases are calculated against different base numbers. The 50% increase was calculated against the original $100. The 50% decrease was calculated against the new, higher $150 — a bigger number, so the same percentage represents a bigger absolute drop than the original increase. Percentages aren't symmetric the way plain addition and subtraction are, which is exactly why "up 50%, down 50%" doesn't return to the start, and why "up X%, down X%" only ever returns to the exact starting point when X is 0.
The related "percentage point" confusion
A second common mix-up: if an interest rate moves from 5% to 7%, that's a 2 percentage point increase, but it's actually a 40% relative increase (2 divided by the original 5, times 100). News headlines sometimes blur this distinction, which can make a change sound bigger or smaller than it really is depending on which framing is used. Always check whether a reported "percent change" is measuring the percentage points moved or the relative size of the change.
Where this matters in real decisions
- Sale stacking: a 20% discount followed by an extra 20% off doesn't total 40% off — it's about 36% off, because the second discount applies to the already-reduced price.
- Investment returns: a portfolio that loses 50% needs a 100% gain (not 50%) just to get back to even, since the loss shrunk the base it needs to grow back from.
- Salary and raise math: a pay cut followed by an "equal percentage" raise later never fully restores the original salary.
Do the math properly
Our Percentage Calculator includes a dedicated increase/decrease mode that calculates the real percentage change between two values, so you can check compounding scenarios like these accurately instead of relying on a gut estimate.