Percentage Calculator
Three Types of Percentage Calculations
1. Percentage of a Number
What is X% of Y?
Example: What is 15% of 200? Answer: 30
2. What Percent?
X is what percent of Y?
Example: 30 is what % of 200? Answer: 15%
3. Percentage Change
What is the % change from X to Y?
Example: Change from 50 to 75? Answer: 50% increase
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 everywhere in daily life: discounts, taxes, tips, grades, statistics, and more.
Percentage Formulas
| Calculation | Formula | Example |
|---|---|---|
| X% of Y | (X/100) × Y | 20% of 150 = 30 |
| X is what % of Y | (X/Y) × 100 | 30 is 20% of 150 |
| % change | ((New-Old)/Old) × 100 | 100→150 = 50% increase |
| Y is X% more than Z | Z × (1 + X/100) | 100 + 20% = 120 |
Converting Percentages
Percent to Decimal
Divide by 100
25% = 0.25
Decimal to Percent
Multiply by 100
0.75 = 75%
Fraction to Percent
Divide, then × 100
3/4 = 75%
Common Percentage Values
| Percent | Decimal | Fraction |
|---|---|---|
| 10% | 0.1 | 1/10 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.3% | 0.333... | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.0 | 1/1 |
Real-World Applications
- Shopping: Calculate sale discounts (30% off a $50 item = $15 savings)
- Tipping: Calculate restaurant tips (15-20% of the bill)
- Taxes: Determine sales tax or income tax amounts
- Grades: Convert test scores to percentages
- Finance: Interest rates, investment returns, loan calculations
- Statistics: Survey results, population changes, growth rates
Quick Tip: Calculating 10%
To quickly find 10% of any number, just move the decimal point one place to the left. For example, 10% of 85 is 8.5. Then you can easily calculate other percentages: 5% is half of that (4.25), 20% is double (17), etc.
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Frequently Asked Questions
How do you calculate a percentage of a number?
Multiply the number by the percentage divided by 100. For 20% of 150: 150 x (20/100) = 150 x 0.2 = 30. Shortcut: move the decimal two places left in the percentage and multiply. 20% becomes 0.20.
What is the formula for percentage increase or decrease?
Percentage change = ((New Value - Old Value) / Old Value) x 100. If a price goes from $50 to $75: ((75-50)/50) x 100 = 50% increase. If it drops to $40: ((40-50)/50) x 100 = -20% (20% decrease).
How do you calculate what percent one number is of another?
Divide the part by the whole and multiply by 100. 'What percent is 30 of 150?' Answer: (30/150) x 100 = 20%. This tells you the proportion of the whole that the part represents.
Why doesn't a 50% increase followed by 50% decrease return to the original?
Because the percentages are calculated from different bases. Starting at $100, a 50% increase gives $150. A 50% decrease of $150 is $75, not $100. The decrease is calculated from the larger number. You need a 33.3% decrease to return to $100 from $150.