The core percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 20% of 250 = 50 |
| X is what percent of Y? | (X ÷ Y) × 100 | 30 of 120 = 25% |
| X is P% of what? | X ÷ (P ÷ 100) | 30 is 25% of 120 |
| Percentage change | ((new − old) ÷ old) × 100 | 50 to 65 = 30% |
| Percentage difference | |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 | 80 vs 100 ≈ 22.22% |
| Increase a value | value × (1 + P ÷ 100) | 80 + 15% = 92 |
| Decrease a value | value × (1 − P ÷ 100) | 80 − 15% = 68 |
| Reverse an increase | final ÷ (1 + P ÷ 100) | 120 after +20% came from 100 |
| Reverse a decrease | final ÷ (1 − P ÷ 100) | 80 after −20% came from 100 |
| Profit margin | (selling price − cost) ÷ selling price × 100 | Cost 60, sell 100 → 40% |
| Markup | (selling price − cost) ÷ cost × 100 | Cost 60, sell 100 → 66.67% |
Common percentage mistakes
A percentage decrease and the same percentage increase do not cancel each other because the second percentage uses a different base. A fall from 100 to 80 is 20%, but returning from 80 to 100 requires a 25% increase.
Percentage points are also different from percentage change: moving from 10% to 15% is an increase of 5 percentage points but a relative increase of 50%.
Use a calculator
Percentage calculator · Percentage change · Find the whole · Reverse percentage · Percentage points