The short answer
Percent means "per hundred." To find X% of Y, multiply: (X ÷ 100) × Y. To find what percent A is of B, divide and multiply by 100: (A ÷ B) × 100. To find percentage change between two values, use (new − old) ÷ old × 100 — positive means increase, negative means decrease.
Key takeaways
- "Percent of" and "what percent" are inverse operations — one multiplies by a percentage, the other divides to find one.
- Percentage increase and decrease share the same formula, (new − old) ÷ old × 100 — the sign tells you which direction it moved.
- Percentage points and percent change aren't the same thing: going from 5% to 8% is a 3-point rise but a 60% relative increase.
- Percentage change is always relative to the starting (old) value — the same dollar change produces a bigger percentage on a smaller starting number.
The four percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X/100) × Y | 25% of 80 = 20 |
| What % is A of B? | (A/B) × 100 | 15 of 60 = 25% |
| Percentage increase | (new−old)/old × 100 | 100 → 120 = 20% |
| Percentage decrease | (old−new)/old × 100 | 100 → 80 = 20% |
Percentage points vs. percent change
An interest rate moving from 2% to 3% is a 1 percentage point increase — simple subtraction. But relative to where it started, that's a 50% increase ((3−2)/2 × 100). News headlines often blur this distinction, so it's worth checking which one a reported number actually means, especially for rates, scores, and survey results.
Worked example: calculating a discount
An $80 jacket is 25% off. What's the sale price?
Discount amount = $80 × 0.25 = $20
Sale price = $80 − $20 = $60
Or directly: $80 × (1 − 0.25) = $80 × 0.75 = $60
Both paths land on the same $60 — subtracting the discount amount, or multiplying by the "keep" percentage (0.75) directly. The second method skips a step and is handy when stacking multiple discounts.
Common mistakes to avoid
- Assuming a 20% increase followed by a 20% decrease returns to the original value — it doesn't. $100 → $120 (up 20%) → $96 (down 20% of $120), not back to $100.
- Mixing up percentage points with percent change, especially when reading about interest rates, tax rates, or survey results.
- Using the new value instead of the old value as the base when calculating percent change — the starting value is always the denominator.
- Assuming percentages can't exceed 100% — they can, and often do, whenever a value more than doubles.
Related calculators
- Percent Error Calculator — compare a measured value against a known accepted value.
- Ratio Calculator — express the same relationship as a ratio instead of a percentage.
- Fraction Calculator — convert a percentage to its exact fractional form.
- Rounding Calculator — round a percentage result to a clean number of decimal places.