How to Calculate Percentages — Complete Guide with Examples
Percentages come up in everyday life constantly — tipping at a restaurant, calculating a sale discount, figuring out your grade, working out tax on a purchase, or understanding interest on a loan. Despite how often we use them, many people find percentage calculations confusing. This guide breaks down every type of percentage calculation with clear formulas and real examples.
The Three Core Percentage Formulas
Every percentage calculation you'll ever need comes down to three basic formulas:
1. What is X% of Y? → Answer = (X ÷ 100) × Y
2. X is what % of Y? → Answer = (X ÷ Y) × 100
3. X is Y% of what? → Answer = X ÷ (Y ÷ 100)
Formula 1 — What is X% of Y?
This is the most common type. You want to find a percentage of a known number.
Example: What is 20% of $85?
Answer = (20 ÷ 100) × 85 = 0.20 × 85 = $17.00
Real uses: calculating a tip, finding a discount amount, working out sales tax, calculating interest.
Formula 2 — X is What Percent of Y?
You have two numbers and want to know the relationship between them as a percentage.
Example: You scored 43 out of 50 on a test. What percentage is that?
Answer = (43 ÷ 50) × 100 = 86%
Real uses: grade calculations, completion percentages, market share, batting averages.
Formula 3 — X is Y% of What?
You know a value and its percentage, and need to find the original whole.
Example: $36 is 15% of what total?
Answer = 36 ÷ (15 ÷ 100) = 36 ÷ 0.15 = $240
Real uses: reverse-engineering original prices, finding a full salary from a deduction amount.
Percentage Change — Increase and Decrease
Percentage change tells you how much something increased or decreased relative to the original value.
% Change = ((New Value − Old Value) ÷ Old Value) × 100
Positive result = increase. Negative result = decrease.
Example: A product was $80 and is now $95. What's the percentage increase?
% Change = ((95 − 80) ÷ 80) × 100 = (15 ÷ 80) × 100 = 18.75% increase
Common Percentage Quick Reference
| To Calculate | Mental Math Shortcut | Example ($200) |
|---|---|---|
| 10% | Move decimal left one place | $20.00 |
| 5% | Half of 10% | $10.00 |
| 15% | 10% + 5% | $30.00 |
| 20% | Divide by 5 | $40.00 |
| 25% | Divide by 4 | $50.00 |
| 50% | Divide by 2 | $100.00 |
| 1% | Move decimal left two places | $2.00 |
Percentage vs Percentage Points
These two terms are often confused and the difference matters. If an interest rate goes from 2% to 3%, it increased by 1 percentage point but by 50% in relative terms. Percentage points measure absolute change; percentage measures relative change. Politicians and advertisers often use whichever one makes their number look bigger, so it's worth knowing the difference.
Real-World Percentage Examples
| Situation | Calculation | Answer |
|---|---|---|
| 18% tip on $65 dinner | (18÷100) × 65 | $11.70 |
| 30% off $120 jacket | (30÷100) × 120 | $36 saved → $84 final |
| 8.5% tax on $50 | (8.5÷100) × 50 | $4.25 tax |
| Score of 38/45 | (38÷45) × 100 | 84.4% |
| Salary increase from $60k to $65k | ((65k−60k)÷60k) × 100 | 8.33% raise |
| $15 is what % of $75? | (15÷75) × 100 | 20% |
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