Percentage Calculator
Calculate percentages, increases, decreases, and changes.
Understanding Percentages
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used extensively in everyday life, from calculating discounts and tips to analyzing business growth and financial returns.
Types of Percentage Calculations
1. Finding What Percentage One Number is of Another
This calculation answers the question: "X is what percent of Y?"
Formula: (Part / Whole) × 100
Example: 30 is what percent of 200?
(30 / 200) × 100 = 15%
2. Finding What X% of a Number Is
This calculates: "What is X% of Y?"
Formula: (Percentage / 100) × Number
Example: What is 15% of 200?
(15 / 100) × 200 = 30
3. Calculating Percentage Change
This determines the percentage increase or decrease between two values.
Formula: ((New Value - Original Value) / Original Value) × 100
Example: Percent change from 100 to 120:
((120 - 100) / 100) × 100 = 20% increase
Common Uses of Percentages
| Application | Example | Calculation |
|---|---|---|
| Sales Tax | 7.5% tax on $100 | $100 × 0.075 = $7.50 tax |
| Discounts | 20% off $50 item | $50 × 0.20 = $10 discount |
| Tips/Gratuity | 18% tip on $75 meal | $75 × 0.18 = $13.50 tip |
| Interest Rates | 5% annual interest | $1000 × 0.05 = $50 interest |
| Business Growth | Revenue growth | Year-over-year comparison |
| Test Scores | 42 out of 50 questions | (42/50) × 100 = 84% |
Percentage Tips and Tricks
Quick Mental Math
- 10%: Move decimal point one place left (10% of 230 = 23)
- 1%: Move decimal point two places left (1% of 230 = 2.3)
- 5%: Find 10% and divide by 2 (5% of 230 = 11.5)
- 15%: Find 10% and add half of it (15% of 230 = 23 + 11.5 = 34.5)
- 20%: Find 10% and double it (20% of 230 = 46)
- 50%: Divide by 2 (50% of 230 = 115)
Common Percentage Pitfalls
- If something increases by 50%, you need a 33.3% decrease to return to the original
- Example: $100 + 50% = $150, then $150 - 33.3% ≈ $100
- A 100% increase doubles the value, but a 50% decrease halves it
Business and Financial Applications
Profit Margins
Calculate how much profit you make as a percentage of sales:
Gross Profit Margin: (Revenue - Cost) / Revenue × 100
If you sell for $150 what cost you $100: ($150 - $100) / $150 × 100 = 33.3%
Return on Investment (ROI)
Measure the profitability of an investment:
ROI Formula: (Gain - Cost) / Cost × 100
Invest $1,000, gain $1,200: ($1,200 - $1,000) / $1,000 × 100 = 20% ROI
Year-Over-Year Growth
Compare performance across time periods:
YoY Growth: (This Year - Last Year) / Last Year × 100
Revenue last year: $500K, this year: $600K: ($600K - $500K) / $500K × 100 = 20% growth
Percentage in Statistics
Percentages are fundamental in statistics and data analysis:
- Percentiles: Indicate the value below which a percentage of data falls (e.g., 90th percentile)
- Confidence Intervals: Express the reliability of estimates (e.g., 95% confidence)
- Market Share: Company's sales as percentage of total market
- Survey Results: Responses expressed as percentages of total
Converting Between Formats
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 66.67% | 0.6667 | 2/3 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
Quick Reference
Basic Formulas:
- Percentage = (Part/Whole) × 100
- Part = (Percentage/100) × Whole
- Whole = Part / (Percentage/100)
Common Percentages
- 10% = 1/10
- 12.5% = 1/8
- 20% = 1/5
- 25% = 1/4
- 33.33% = 1/3
- 50% = 1/2
- 66.67% = 2/3
- 75% = 3/4