Three Types of Percentage Calculations
There are three fundamental percentage questions, each with its own formula:
1. What is X% of Y? Formula: Result = (X/100) × Y. Example: What is 15% of $80? 0.15 × $80 = $12.
2. X is what percent of Y? Formula: % = (X/Y) × 100. Example: $12 is what percent of $80? (12/80) × 100 = 15%.
3. Percent change from X to Y? Formula: % Change = [(Y−X)/X] × 100. Example: Price changes from $80 to $96: (96−80)/80 × 100 = 20% increase.
Confusing these three questions is the source of most percentage errors. Always identify which type of question you're answering before applying a formula.
Quick Mental Math for Common Percentages
Mental shortcuts make percentage math fast:
10% of any number: move the decimal one place left. 10% of 347 = 34.7. 5% = half of 10%. 5% of 347 = 17.35. 1% = move decimal two places left. 1% of 347 = 3.47. 20% = double the 10% value. 20% of 347 = 69.4. 25% = divide by 4. 25% of 200 = 50. 75% = 3/4 of the number. 75% of 200 = 150. 15% (restaurant tip shortcut): find 10%, then add half. 10% of $53 = $5.30, plus $2.65 = $7.95 total tip.