Bottom Line Up Front (BLUF): Calculating Percentages
A percentage represents a fraction of 100 ('per cent' = per hundred). To find P% of X, multiply (P / 100) × X. To find what percentage X is of Y, divide (X / Y) × 100. To find percentage change from A to B, calculate ((B - A) / |A|) × 100.
Core Percentage Formulas & Methods
1. Percentage of a Number (P% of X)
Formula: Result = (P / 100) × X. For example, 15% of $80 = (15 / 100) × 80 = 0.15 × 80 = $12.00.
2. Percentage Ratio (X is what % of Y?)
Formula: Percentage = (X / Y) × 100%. For example, if you scored 24 out of 96 questions on an exam, (24 / 96) × 100% = 0.25 × 100% = 25%.
3. Percentage Increase / Decrease (Change from A to B)
Formula: Change % = ((New - Old) / |Old|) × 100%. If revenue grows from $50,000 to $75,000: (($75,000 - $50,000) / $50,000) × 100% = +50% increase.
4. Discount & Sales Tax Calculation
Discounted Price = Original × (1 - Discount%). Final Total = Discounted Price × (1 + Tax%). For a $100 item with 20% discount and 8% tax: $80 × 1.08 = $86.40.
Common Percentage Multipliers Quick Reference
| Percentage | Fraction | Decimal Multiplier | Example ($100 Base) |
|---|---|---|---|
| 5% | 1/20 | 0.05 | $5.00 |
| 10% | 1/10 | 0.10 | $10.00 |
| 15% | 3/20 | 0.15 | $15.00 (Standard Tip) |
| 20% | 1/5 | 0.20 | $20.00 (Retail Discount) |
| 25% | 1/4 | 0.25 | $25.00 (Quarter) |
| 33.33% | 1/3 | 0.3333 | $33.33 (One-Third) |
| 50% | 1/2 | 0.50 | $50.00 (Half) |
| 75% | 3/4 | 0.75 | $75.00 (Three-Quarters) |
Frequently Asked Questions about Percentages
How do I calculate a 20% tip quickly in my head?
Find 10% by moving the decimal point one place to the left, then double that number. For a $45.00 bill: 10% is $4.50; 20% is $4.50 × 2 = $9.00.
What is the difference between percentage points and percentage change?
Percentage points is the simple arithmetic difference (e.g. from 10% to 15% is a 5 percentage point increase), whereas percentage change is relative to the starting value: ((15 - 10) / 10) × 100% = 50% relative increase.
Can percentage change exceed 100%?
Yes. An increase from 10 to 30 represents a +200% increase (it tripled in size, meaning it increased by two times the original amount).