How to Calculate Percentage: Formulas, Shortcuts & Real Examples
To find a percentage of a number: multiply the number by the percentage and divide by 100. Example: 25% of 80 = 80 × 25 ÷ 100 = 20. For percentage change: ((New − Old) ÷ Old) × 100.
The Three Fundamental Percentage Formulas
Every percentage question falls into one of three categories. Master these three formulas and you can solve any percentage problem:
Mental Math Shortcuts for Common Percentages
You don't always need a calculator. These mental math tricks let you estimate percentages instantly:
| Percentage | Mental Shortcut | Example (of $160) |
|---|---|---|
| 1% | Move decimal 2 places left | $1.60 |
| 10% | Move decimal 1 place left | $16.00 |
| 15% | 10% + half of 10% | $24.00 |
| 20% | 10% × 2 | $32.00 |
| 25% | Divide by 4 | $40.00 |
| 33% | Divide by 3 | $53.33 |
| 50% | Divide by 2 | $80.00 |
| 75% | Subtract 25% from whole | $120.00 |
Real-World Percentage Applications
Tipping: 20% of an $85 dinner bill — 10% is $8.50, double it = $17.00 tip. Discounts: 30% off a $79.99 item — 10% is $8, × 3 = $24 off, final price ≈ $56. Tax: 8.5% sales tax on $200 — 10% is $20, minus 1.5% ($3) = $17 tax. Grades: Scored 42 out of 50 — (42 ÷ 50) × 100 = 84%.
Common Percentage Mistakes to Avoid
Percentage increase ≠ percentage decrease. If a $100 item increases by 50% it becomes $150. But a 50% decrease from $150 is $75, not back to $100. This is because the base number changes. A 50% increase followed by a 50% decrease always results in a 25% net loss.
Double discounts are not additive. "20% off + extra 10% off" is NOT 30% off. It is 20% off first ($100 → $80), then 10% off that ($80 → $72). Effective discount: 28%, not 30%.
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