Percentages appear everywhere — in discounts, tax rates, exam grades, interest rates, nutrition labels, and statistics. Yet many adults are unsure which formula to use in each situation. This guide covers the four core percentage calculations with clear, practical examples.
What "Percent" Means
"Percent" literally means "per hundred." A percentage is simply a ratio expressed as a fraction of 100.
15% = 15/100 = 0.15
This means that every percentage calculation ultimately involves multiplying or dividing by 100.
Formula 1: Find the Percentage of a Number
"What is X% of Y?"
Formula: Result = (Percentage ÷ 100) × Number
Example: What is 30% of 250? Result = (30 ÷ 100) × 250 = 0.30 × 250 = 75
Real-world use: A restaurant bill is $80. You want to leave a 15% tip. Tip = 0.15 × 80 = $12
Formula 2: What Percentage Is One Number of Another?
"What % is X of Y?"
Formula: Percentage = (Part ÷ Whole) × 100
Example: You scored 42 out of 60 on a test. What is your percentage? Percentage = (42 ÷ 60) × 100 = 0.70 × 100 = 70%
Real-world use: A store sold 340 units out of a stock of 500. Sell-through rate = (340 ÷ 500) × 100 = 68%
Formula 3: Percentage Change
"By what % did X change from one value to another?"
Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result = increase; a negative result = decrease.
Example: A stock price moves from $50 to $65. % Change = ((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = +30%
Example: Monthly sales drop from 1,200 to 900 units. % Change = ((900 − 1200) ÷ 1200) × 100 = (−300 ÷ 1200) × 100 = −25%
Formula 4: Reverse Percentage (Find the Original Value)
"If Y is X% of the original, what was the original?"
Formula: Original = Value ÷ (Percentage ÷ 100)
Example: A coat is on sale for $85 after a 15% discount. What was the original price? Original = 85 ÷ (1 − 0.15) = 85 ÷ 0.85 = $100
Example: A salary after a 20% tax deduction is $40,000. What was the gross salary? Gross = 40,000 ÷ 0.80 = $50,000
Quick Reference: Common Percentage Conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333 | 33.3% |
| 1/2 | 0.50 | 50% |
| 2/3 | 0.667 | 66.7% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.20 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.10 | 10% |
Mental Math Shortcuts
- 10%: Move the decimal one place left. 10% of 340 = 34
- 5%: Half of 10%. 5% of 340 = 17
- 20%: Double of 10%. 20% of 340 = 68
- 25%: Divide by 4. 25% of 340 = 85
- 15%: 10% + 5%. 15% of 340 = 34 + 17 = 51
Calculate Percentages Instantly
For any percentage problem — from calculating tax on an invoice to tracking year-over-year growth — our Percentage Calculator handles all four formulas with a single interface. Enter two values, select your calculation type, and get an instant result.
Frequently Asked Questions
Q: What is the formula for finding X% of a number? A: Result = (Percentage ÷ 100) × Number — for example, 30% of 250 is (30 ÷ 100) × 250 = 75.
Q: How do I find what percentage one number is of another? A: Use Percentage = (Part ÷ Whole) × 100; scoring 42 out of 60 on a test equals (42 ÷ 60) × 100 = 70%.
Q: How can I quickly estimate a 15% tip in my head? A: Find 10% by moving the decimal one place left, then add half of that for 5% — e.g., 15% of $340 is $34 + $17 = $51.
