30% off is how much? When percentages keep tripping you up
Everyday percentages — discounts, tax, and change over time — trip people up because one word, 'percent,' covers three different calculations. Here's how to tell them apart and avoid the classic mistake of adding and subtracting percentages.
The problem: you reach for the calculator at every sale
"30% off" doesn't always translate into a number instantly. What's the final price once tax is added? How do you work out how many percent sales "grew" over last year? You learned percentages in grade school, yet they trip you up in daily life — because we lump three different calculations under the single word "percent."
Separate the three and the confusion disappears: ① what a given percent of a total is, ② what percent A is of B, and ③ how much a value went up or down (percent change).
The three percentage calculations
① A percent of a total: multiply the base by the percent and divide by 100. 30% of $30 is 30 × 30 ÷ 100 = $9. A sale price goes one step further: $30 − $9 = $21.
② What percent A is of B: divide A by B and multiply by 100. 45 is 45 ÷ 200 × 100 = 22.5% of 200 — used for completion rates and shares. ③ Percent change: divide (new − old) by the old value and multiply by 100. From 100 to 130 is (130−100)÷100×100 = a 30% increase.
| Type | Formula | Example |
|---|---|---|
| Percent of a total | base × % ÷ 100 | 30% of 30,000 = 9,000 |
| Sale price | base − (base × % ÷ 100) | 30% off 30,000 = 21,000 |
| A is what % of B | A ÷ B × 100 | 45 is 22.5% of 200 |
| Percent change | (new − old) ÷ old × 100 | 100→130 = +30% |
The common mistake: does up-then-down cancel out?
The most common trap is adding and subtracting percent changes. If $100 rises 50% to $150, then falls 50%, you might expect $100 — but it's actually $75, because the second 50% is taken from $150, not $100.
Likewise, "20% off then an extra 10% off" is not 30% off. You take 90% of the remaining 80%, which is 72% — a 28% discount. Always check "percent of what" to avoid the error.
In short
Percentages confuse people not because it's hard math but because three different calculations hide behind one word. Decide first whether you mean 'a percent of a total,' 'what share something is,' or 'how much it changed,' and in change or stacked discounts, check the base value. That alone removes most mistakes.
Frequently asked questions
How do I get a tax-included price?
Add the tax percent to the base. At 10%, a $10 item is 10 × 1.1 = $11 including tax. To go back, divide the tax-included $11 by 1.1 to get the $10 base.
Is "30% off then an extra 10%" a 40% discount?
No. You take 90% of the remaining 70%, which is 63% — a 37% discount. Stacked discounts multiply, they don't add.
What if the percent change is negative?
If the new value is smaller than the old one, it decreased, so it shows as negative (−). From 200 to 150 is (150−200)÷200×100 = −25%.