Percentages: 7 Common Mistakes (and How to Avoid Them)
Percent vs percentage points, why a 50% drop needs a 100% rise, how discounts stack, VAT backwards and other everyday percentage traps, with simple examples.
Percentages appear in prices, salaries, interest rates, statistics and headlines, and they are misunderstood surprisingly often, sometimes by accident and sometimes on purpose. These are the seven mistakes we see most, with examples you can check in the percentage calculator.
1. Percent vs percentage points
If an interest rate rises from 2 percent to 3 percent, it rose by 1 percentage point, but by 50 percent relative to where it was. Both statements are true, and they sound very different. News stories and marketing often choose whichever sounds more dramatic. When you compare rates, ask which one is meant.
2. Up and down are not symmetric
A share price falls 50 percent, from 100 to 50. To get back to 100, it must rise by 100 percent, not 50. Likewise, a 20 percent pay cut followed by a 20 percent raise leaves you at 96 percent of your original salary: 100 × 0.8 × 1.2 = 96. Losses always need bigger percentage gains to recover.
3. Discounts do not add up
“20 percent off, plus an extra 10 percent at the checkout” is not 30 percent off. The second discount applies to the already reduced price: 100 × 0.8 × 0.9 = 72, which is 28 percent off. Shops know that “20% + 10%” sounds bigger than “28%”.
4. Removing VAT or sales tax
A price of 120 includes 20 percent VAT. The price before tax is not 120 minus 20 percent (96), but 120 divided by 1.2, which is 100. The tax was 20 percent of the net price, not of the total. The same applies to any “price including a markup”: divide by (1 + rate), do not subtract.
5. Margin vs markup
You buy a product for 80 and sell it for 100. The markup is 25 percent (20 on top of the cost of 80). The margin is 20 percent (20 of the selling price of 100). Mixing the two in a business plan quietly turns a profitable price into a loss-making one. Always say which base you are using.
6. Small bases make big percentages
“Sales up 300 percent!” sounds impressive until you learn they went from 2 units to 8. “Risk doubled” may mean a change from 1 in 100,000 to 2 in 100,000. Whenever you see a big percentage change, ask for the absolute numbers behind it.
7. Averaging percentages
A shop converts 10 percent of 1,000 visitors on Monday and 50 percent of 10 visitors on Tuesday. The average of the two rates is 30 percent, but the real conversion rate over both days is (100 + 5) / 1,010, about 10.4 percent. Averages of percentages are only meaningful when the bases are equal. Otherwise, add up the underlying counts first.
A few quick formulas
- X percent of Y: Y × X / 100
- X is what percent of Y: X / Y × 100
- Percentage change from A to B: (B − A) / A × 100
- Add X percent: Y × (1 + X / 100)
- Remove an included X percent: Y / (1 + X / 100)
Our take
Every percentage has a base, and almost every percentage mistake comes from forgetting which one. Before you trust or quote a percentage, ask “percent of what?” That single question protects you from misleading discounts, alarming headlines and broken spreadsheets.