The Three Percentage Problems
Nearly every percentage question is one of three patterns — this calculator covers all of them:
| Question | Formula | Example |
|---|---|---|
| What is 25 % of 200? | (25 ÷ 100) × 200 | 50 |
| 50 is what % of 200? | (50 ÷ 200) × 100 | 25 % |
| Change from 200 to 250? | ((250 − 200) ÷ 200) × 100 | +25 % |
Percent Change: The Direction Matters
Percent change is always relative to the starting value. Going from 200 to 250 is +25 %, but going from 250 back to 200 is −20 %. That asymmetry trips people up constantly — a 50 % loss needs a 100 % gain to recover.
Everyday Shortcuts
- 10 % : shift the decimal point — 10 % of 84 is 8.4.
- 5 % : half of 10 %. 1 % : shift twice.
- Reverse trick: X % of Y always equals Y % of X. 8 % of 25 feels hard; 25 % of 8 is obviously 2.
- Percentage points ≠ percent: a rate rising from 4 % to 6 % climbs 2 percentage points but 50 percent.