The one thing people get wrong: percentage change is not reversible
Increase 80 by 25% and you get 100. It feels like decreasing 100 by 25% should bring you back to 80 — it doesn't. It lands on 75. The reason is that each percentage is taken of a different base: the +25% was taken of 80, but the −25% is taken of the bigger number, 100, so it removes more than the first step added. Only the exact reverse percentage undoes a change (100 would need to drop by 20%, not 25%, to get back to 80) — which is exactly why stacked discounts don't add the way people expect either; it's the same asymmetry in different clothing.
A related mix-up: a "percentage point" is not a "percentage change." If a tax rate moves from 5% to 6%, that's a 1 percentage point increase (plain subtraction) but a 20% relative percentage change ((6−5)÷5×100). Both numbers are correct and both get reported in the news — usually whichever one makes the story sound bigger.
The four formulas
Worked examples, one per mode
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 150? | 150 × 20 ÷ 100 | 30 |
| 45 is what percent of 180? | 45 ÷ 180 × 100 | 25% |
| Percentage change from 80 to 100? | (100 − 80) ÷ 80 × 100 | +25% (increase) |
| Increase 200 by 15%? | 200 × 1.15 | 230 |
Frequently asked questions
How do I calculate what X% of Y is?
Multiply Y by X and divide by 100: result = Y × X ÷ 100. 20% of 150 is 150 × 20 ÷ 100 = 30.
How do I calculate what percent one number is of another?
Divide the part by the whole and multiply by 100: percent = part ÷ whole × 100. 45 is what percent of 180? 45 ÷ 180 × 100 = 25%.
What is "percentage change" and how is it calculated?
(new − old) ÷ old × 100. Going from 80 to 100 is +25%. Going from 100 back to 80 is −20%, not the same 25%, because the base you're dividing by is different each direction.
If something increases 25% and then decreases 25%, does it end up back where it started?
No. 80 up 25% is 100; 100 down 25% is 75, not 80. The second 25% is taken off a bigger number than the first 25% was added to. Only the exact reverse percentage (here, 20%) undoes it.
What's the difference between a percentage change and a percentage POINT change?
A percentage point difference is plain subtraction: 5% to 6% is 1 point. A percentage change is relative to the start: (6−5)÷5×100 = 20%. Both are correct; they answer different questions.
How do I increase or decrease a number by a percentage?
Increase: multiply by (1 + percent ÷ 100). Decrease: multiply by (1 − percent ÷ 100). 200 increased 15% is 230; decreased 15% is 170.
Can a percentage be negative or over 100%?
Yes to both. Over 100% just means "more than the whole" — 150% of 40 is 60. The percentage-change mode reports direction (increase/decrease) alongside the number so a negative result is never ambiguous.