The Percentage Mistake Everyone Makes At Least Once

Here's a question that trips up almost everyone the first time: a shirt goes up 20% in price, then goes on sale for 20% off. Is it back to the original price?

No. And the reason why is the entire idea behind why the Percentage Calculatortreats "increase" and "decrease" as genuinely different operations, not mirror images of each other.

If a $100 shirt goes up 20%, it's $120. Take 20% off $120, and you get $96 — not $100. The second 20% is calculated on a bigger number than the first one was, so it removes more in absolute terms than the first increase added... except it doesn't, because percentages of different base numbers aren't comparable the way flat amounts are. This asymmetry is the single most common source of percentage-math errors we see reflected in how people use the tool — repeatedly checking "did I get this right?" on decrease-then-increase or increase-then-decrease sequences.

The fix wasn't a better explanation. It was separating "percentage of," "percentage change," and "what percent is X of Y" into three distinct, clearly labeled calculator modes, so the tool never lets you accidentally use the wrong formula for the question you're actually asking.