Percentage Calculator - Free Online Percentage Calculator with Formulas and Examples
Percentage Calculator in Common Phrases
Percentage Difference Calculator
Percentage Change Calculator
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Understanding Percentage Calculations
🔢What is a Percentage?
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 in everyday life to express proportions, compare values, and calculate changes in quantities.
For example, 50% means 50 out of 100, or half. Percentages are essential in finance, statistics, science, and many other fields where we need to compare different quantities on a standardized scale.
📐Basic Percentage Formulas
Find the Percentage:
(Part ÷ Whole) × 100 = Percentage
Calculate Percent of Value:
(Percent ÷ 100) × Value = Result
Percentage Change:
((New - Old) ÷ Old) × 100 = % Change
🛍️Percentages in Daily Life
Percentages are everywhere in our daily lives:
- • Shopping: Sales discounts (30% off), sales tax (8.5%)
- • Finance: Interest rates (4% APR), investment returns (12% annually)
- • Health: Body fat percentage, daily nutrient values
- • Education: Test scores (95%), grade percentages
- • Statistics: Population growth, survey results
💡Quick Calculation Tips
- • 10%: Move decimal point one place left (10% of 50 = 5)
- • 50%: Divide by 2 (50% of 80 = 40)
- • 25%: Divide by 4 (25% of 100 = 25)
- • 5%: Calculate 10% and divide by 2
- • 1%: Divide by 100 (1% of 200 = 2)
- • Convert to decimal: Divide percent by 100 (75% = 0.75)
Common Percentage Conversions
| Percentage | Decimal | Fraction | Example (of 100) |
|---|---|---|---|
| 10% | 0.10 | 1/10 | 10 |
| 25% | 0.25 | 1/4 | 25 |
| 50% | 0.50 | 1/2 | 50 |
| 75% | 0.75 | 3/4 | 75 |
| 100% | 1.00 | 1/1 | 100 |
Frequently Asked Questions
How do you calculate percentage?
To calculate a percentage, divide the part by the whole and multiply by 100. For example, to find what percent 25 is of 100: (25 ÷ 100) × 100 = 25%. You can also calculate X% of Y by multiplying: (X ÷ 100) × Y.
What is 20% of 100?
20% of 100 is 20. To calculate this, multiply 100 by 0.20 (which is 20% as a decimal), or use the formula: (20 ÷ 100) × 100 = 20.
How do you calculate percentage increase?
To calculate percentage increase: 1) Find the difference between the new and original value, 2) Divide the difference by the original value, 3) Multiply by 100. Formula: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a value increases from 50 to 75: ((75 - 50) ÷ 50) × 100 = 50% increase.
How do you calculate percentage decrease?
To calculate percentage decrease, use the same formula as percentage increase but the result will be negative: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a value decreases from 100 to 80: ((80 - 100) ÷ 100) × 100 = -20% (a 20% decrease).
What is the difference between percentage and percent?
There is no mathematical difference between 'percentage' and 'percent' - they mean the same thing. 'Percent' is typically used with numbers (e.g., '50 percent'), while 'percentage' is often used as a noun (e.g., 'What percentage is this?'). Both represent a fraction of 100.
How do you find what number a percentage represents?
To find what number a percentage represents (e.g., '25 is 25% of what?'), divide the part by the percentage (as a decimal). Formula: Part ÷ (Percent ÷ 100) = Whole. For example: 25 ÷ 0.25 = 100. So 25 is 25% of 100.
What is percentage difference and how do you calculate it?
Percentage difference measures the relative change between two values. Formula: |Value1 - Value2| ÷ ((Value1 + Value2) ÷ 2) × 100. For example, the percentage difference between 100 and 120 is: |100-120| ÷ ((100+120)÷2) × 100 = 18.18%. This is useful for comparing prices, measurements, or statistics.
How do you calculate discount percentage?
To calculate discount percentage: ((Original Price - Sale Price) ÷ Original Price) × 100. For example, if an item costs $100 and is on sale for $75, the discount is ((100-75)÷100)×100 = 25% off. You can also calculate the final price by subtracting the discount percentage: $100 - (25% of $100) = $75.