Percentage Calculator
A versatile percentage calculator that can handle common percentage calculations, percentage changes, and differences between numbers. Perfect for financial calculations, statistics, and everyday math.
Percentage Calculator
Calculate percentages, changes, and differences
Percentage Calculation Results
Based on your input values
25% of 100 is:
25.00
Formula: (25 ÷ 100) × 100
Visual Representation
25% of 100 = 25
What This Means
This calculation finds a specified percentage of a value. You've calculated 25% of 100, which means 0.25 times 100.
Applications
- Calculate discounts (e.g., 20% off a $100 item)
- Determine taxes (e.g., 7% sales tax on a purchase)
- Figure out tips (e.g., 15% tip on a restaurant bill)
Understanding Percentage Calculations
Learn more about various percentage calculations and their applications
Understanding Percentages
The word "percentage" comes from "per centum" which means "per hundred" in Latin. A percentage is a way to express a number as a fraction of 100, making it easier to compare relative values.
Basic Concepts
- 100% represents the whole or total amount
- 50% is half of the total
- 25% is one quarter of the total
- 1% is one hundredth of the total
- 200% is twice the total
Converting Between Formats
| Percentage | Decimal | Fraction |
|---|---|---|
| 100% | 1.0 | 1 |
| 75% | 0.75 | 3/4 |
| 50% | 0.5 | 1/2 |
| 25% | 0.25 | 1/4 |
| 20% | 0.2 | 1/5 |
| 10% | 0.1 | 1/10 |
| 1% | 0.01 | 1/100 |
Common Calculations
Finding a Percentage of a Number
To find X% of Y:
X% of Y = (X ÷ 100) × Y
Example: What is 25% of 80?
- Write the percentage as a decimal: 25% = 25 ÷ 100 = 0.25
- Multiply by the number: 0.25 × 80 = 20
- Result: 25% of 80 is 20
Finding What Percentage One Number is of Another
To find what percentage X is of Y:
X is (X ÷ Y) × 100% of Y
Example: 20 is what percentage of 80?
- Divide the first number by the second: 20 ÷ 80 = 0.25
- Multiply by 100 to convert to a percentage: 0.25 × 100 = 25%
- Result: 20 is 25% of 80
Calculating Percentage Change
To find the percentage change from X to Y:
Percentage Change = ((Y - X) ÷ X) × 100%
Example: What is the percentage change from 80 to 100?
- Find the difference: 100 - 80 = 20
- Divide by the original value: 20 ÷ 80 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
- Result: The percentage change from 80 to 100 is a 25% increase
Finding Percentage Difference
To find the percentage difference between X and Y:
Percentage Difference = (|X - Y| ÷ ((X + Y) ÷ 2)) × 100%
Example: What is the percentage difference between 80 and 100?
- Find the absolute difference: |80 - 100| = 20
- Find the average: (80 + 100) ÷ 2 = 90
- Divide the difference by the average: 20 ÷ 90 = 0.222...
- Multiply by 100: 0.222... × 100 = 22.22...%
- Result: The percentage difference between 80 and 100 is 22.22...%
Note: Unlike percentage change, percentage difference is always positive and treats both values equally.
Real-World Applications
Finance and Business
- Discounts and Sales: "20% off" means the price is reduced by 20% of the original price
- Interest Rates: Banks express interest as a percentage of the principal amount
- Tax Calculations: Sales tax, income tax, and other taxes are calculated as percentages
- Growth Rates: Business metrics like revenue growth are expressed as percentage changes
- Profit Margins: The percentage of revenue that becomes profit
Education
- Grading: Test scores are often expressed as percentages (90% = A, 80% = B, etc.)
- Class Rankings: Students might be in the "top 10%" of their class
- Attendance Rates: Schools track attendance as a percentage of total school days
- Improvement Metrics: Student progress is often measured as a percentage improvement
Science and Statistics
- Chemical Concentrations: Solutions are often described by percentage concentration
- Statistical Significance: Results are considered significant at certain percentage thresholds
- Experimental Error: Margin of error in experiments is expressed as a percentage
- Probability: The chance of an event occurring can be expressed as a percentage
Health and Fitness
- Body Fat Percentage: The proportion of body mass that is fat
- Nutritional Information: Daily values on food labels are shown as percentages
- Heart Rate Zones: Training zones are often calculated as percentages of maximum heart rate
- Weight Loss Goals: Often specified as a percentage of starting weight
Tips and Common Mistakes
Tips for Working with Percentages
- Convert percentages to decimals by dividing by 100 (e.g., 25% = 0.25)
- For a percentage increase, multiply by (1 + percentage/100) (e.g., 20% increase: multiply by 1.2)
- For a percentage decrease, multiply by (1 - percentage/100) (e.g., 20% decrease: multiply by 0.8)
- To find the original value after a percentage change, divide by (1 + percentage change/100)
- Percentage points and percentages are different concepts, especially in finance and statistics
Calculation Shortcuts
- Finding 10%: Just move the decimal point one place to the left (e.g., 10% of 250 = 25)
- Finding 1%: Move the decimal point two places to the left (e.g., 1% of 250 = 2.5)
- Finding 5%: Find 10% and divide by 2 (e.g., 5% of 250 = 25 ÷ 2 = 12.5)
- Finding 20%: Find 10% and multiply by 2 (e.g., 20% of 250 = 25 × 2 = 50)
- Finding 25%: Divide by 4 (e.g., 25% of 250 = 250 ÷ 4 = 62.5)
- Finding 50%: Divide by 2 (e.g., 50% of 250 = 250 ÷ 2 = 125)
- Finding 33.33%: Divide by 3 (e.g., 33.33% of 250 = 250 ÷ 3 = 83.33)
Command Palette
Search for a command to run...