Percentages show up everywhere — discounts, test scores, tax rates, salary increases, and interest rates. Most people can handle simple cases but get confused when the question is phrased differently. Here are the three calculations that cover almost every situation.
Method 1: What Is X% of Y?
This is the most common type. "What is 20% of $85?" or "What is 15% of 240?"
Formula: result = (percentage ÷ 100) × total
Examples:
- 20% of $85 = 0.20 × 85 = $17
- 15% of 240 = 0.15 × 240 = 36
- 7.5% of $320 = 0.075 × 320 = $24
Mental math shortcut: To find 10%, divide by 10. To find 5%, take half of 10%. To find 20%, double the 10% result. To find 15%, add 10% and 5% together.
Method 2: X Is What Percent of Y?
This type answers: "I scored 34 out of 40 — what percentage is that?" or "My rent is $1,200 and my income is $4,500 — what percentage goes to rent?"
Formula: percentage = (part ÷ whole) × 100
- 34 out of 40 = (34 ÷ 40) × 100 = 85%
- $1,200 of $4,500 = (1200 ÷ 4500) × 100 = 26.7%
- 18 out of 75 = (18 ÷ 75) × 100 = 24%
Method 3: Percentage Change
This answers: "Prices went from $80 to $96 — what percentage increase is that?" or "Sales dropped from 500 to 425 — what was the percentage decrease?"
Formula: % change = ((new − old) ÷ old) × 100
- $80 to $96: ((96 − 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = +20%
- 500 to 425: ((425 − 500) ÷ 500) × 100 = (−75 ÷ 500) × 100 = −15%
A positive result means an increase; negative means a decrease.
Common Percentages Quick Reference
| To Find | Operation | Example on $200 |
|---|---|---|
| 1% | Divide by 100 | $2 |
| 5% | Divide by 20 | $10 |
| 10% | Divide by 10 | $20 |
| 20% | Divide by 5 | $40 |
| 25% | Divide by 4 | $50 |
| 50% | Divide by 2 | $100 |
| 75% | Multiply by 0.75 | $150 |
Working Backwards: Finding the Original Price
A common trap: a jacket is on sale for $68 after a 20% discount. What was the original price? Many people subtract 20% from $68 and get it wrong. The correct method:
After a 20% discount, you paid 80% of the original. So: original = sale price ÷ 0.80 = 68 ÷ 0.80 = $85
The rule: divide by the decimal form of the remaining percentage (100% minus the discount %).
Calculate any percentage instantly — what is X% of Y, percentage change, and more
Use the Percentage Calculator →Key Takeaways
- X% of Y: multiply Y by (X÷100)
- X is what % of Y: divide X by Y, multiply by 100
- Percentage change: (new − old) ÷ old × 100
- Find the original: divide by the remaining percentage as a decimal