Three modes: % of a number, % change, and ratio to %.
Percentages represent parts per hundred. Whether you're calculating discounts, grades, tips, or growth rates, these 10 formulas cover every common scenario:
| Percentage | Decimal | Fraction | Common Use |
|---|---|---|---|
| 10% | 0.10 | 1/10 | Quick mental math tip |
| 12.5% | 0.125 | 1/8 | Interest calculations |
| 20% | 0.20 | 1/5 | Restaurant tips |
| 25% | 0.25 | 1/4 | Quarter-year reports |
| 33.33% | 0.333 | 1/3 | Third-split bills |
| 50% | 0.50 | 1/2 | Half-off sales |
| 66.67% | 0.667 | 2/3 | Two-thirds majority |
| 75% | 0.75 | 3/4 | Grade thresholds |
| 100% | 1.00 | 1/1 | Full amount |
| Factor | Percentage | Percentile |
|---|---|---|
| Definition | Part per hundred | Rank relative to others |
| Example | You scored 85/100 = 85% | You ranked above 90% of students = 90th percentile |
| Symbol | % | No standard symbol |
| Used in | Grades, discounts, growth | Standardized tests, height charts |
Percentage increase = ((New Value - Old Value) / Old Value) × 100. For example, if a price went from $50 to $65: ((65-50)/50) × 100 = 30% increase.
15% of 200 = 200 × (15/100) = 200 × 0.15 = 30. Mental math shortcut: find 10% (20) + 5% (10) = 30.
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.
Percentage difference = |Value1 - Value2| / ((Value1 + Value2) / 2) × 100. This measures how different two values are relative to their average.
Yes! A percentage above 100% means the value exceeds the baseline. For example, if a stock went from $50 to $150, that's a 200% increase (the growth is 2x the original).
Add up your total marks obtained across all subjects, divide by the total maximum marks, then multiply by 100. Example: 420 out of 500 = (420/500) × 100 = 84%.
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