A percentage represents a number out of 100. The word comes from Latin "per centum" meaning "by the hundred."
Key Formulas
- Finding a percentage: (Part ÷ Whole) × 100
- Finding part from percentage: Whole × (Percentage ÷ 100)
- Percentage change: ((New - Old) ÷ Old) × 100
Examples
What is 15% of 200? → 200 × 0.15 = 30
25 is what percent of 80? → (25 ÷ 80) × 100 = 31.25%
Percentage Points vs. Percent
A common source of confusion: if a rate rises from 20% to 25%, that's a 5 percentage point increase, but a 25% relative increase (5 ÷ 20 = 25%). News headlines often blur this distinction — always check whether a reported change is in percentage points or relative percent, since they can tell very different stories from the same numbers.
Reverse Percentage (Finding the Original Value)
If a discounted price of $85 reflects a 15% discount, the original price is found by dividing, not subtracting: Original = 85 ÷ (1 − 0.15) = 85 ÷ 0.85 = $100. A common mistake is adding 15% to $85 instead, which gives the wrong answer ($97.75).