Percentage Change Calculator
Calculate the percentage increase or decrease between an original value and a new value. Essential for analyzing growth, discounts, trends, and financial performance.
Calculate Percentage Change
Enter the original value and the new value to calculate the percentage change:
Change = ((New - Original) / |Original|) × 100%
Positive = increase, Negative = decrease
Understanding Percentage Change
Percentage change is a fundamental concept used to measure the relative difference between two values. It tells you how much something has increased or decreased as a percentage of the original value, making it easy to compare changes of different magnitudes.
Percentage Change Formula
📈 Basic Formula
% Change = ((New Value - Original Value) / |Original Value|) × 100%
The absolute value ensures positive division
Result shows relative change magnitude
🔍 Interpretation
Positive values = increase
Negative values = decrease
Zero = no change
Larger magnitude = bigger change
💡 Key Insight
Percentage change shows relative impact
Not affected by scale of original values
Essential for comparing different datasets
💡 Pro Tip: Percentage change is more meaningful than absolute change when comparing values of different scales. For example, a $100 increase is huge for a $200 item (50% increase) but tiny for a $20,000 car (0.5% increase).
Common Examples
| Scenario | Original | New | % Change | Interpretation |
|---|---|---|---|---|
| Stock Price | $100 | $125 | +25% | Stock increased 25% |
| Sales Revenue | $50,000 | $45,000 | -10% | Sales decreased 10% |
| Product Price | $99.99 | $79.99 | -20% | 20% discount applied |
| Company Growth | $1,000,000 | $1,200,000 | +20% | Company grew 20% |
| Weight Loss | 200 lbs | 180 lbs | -10% | Lost 10% of body weight |
| Population Growth | 10,000 | 10,500 | +5% | Population increased 5% |
Percentage Change vs Absolute Change
📊 Absolute Change
Simple difference: New - Original
Units match original values
Example: Price increased by $20
Good for: Exact dollar amounts
📈 Percentage Change
Relative difference as percentage
Unitless (always %)
Example: Price increased by 25%
Good for: Comparing different scales
⚖️ When to Use Each
Use absolute for same-scale comparisons
Use percentage for different-scale comparisons
Both together give complete picture
Real-World Applications
📈 Business & Finance
Stock price performance analysis
Sales revenue growth tracking
Profit margin comparisons
Budget variance analysis
Market share changes
💰 Retail & E-commerce
Discount and promotion calculations
Sales performance metrics
Customer acquisition cost changes
Inventory turnover analysis
Seasonal trend comparisons
📊 Data Analysis
Year-over-year growth rates
Market research result analysis
Economic indicator comparisons
Performance metric benchmarking
Trend analysis and forecasting
🏥 Health & Fitness
Weight loss/gain progress tracking
Body fat percentage changes
Fitness goal achievement
Medical test result comparisons
Health metric improvements
Advanced Concepts
| Concept | Formula | Example | Use Case |
|---|---|---|---|
| Compound Growth | Future = Present × (1 + r)^t | $1000 × (1.05)^5 = $1276 | Investment growth |
| CAGR | CAGR = (End/Start)^(1/n) - 1 | (1276/1000)^(1/5) - 1 = 5% | Average annual growth |
| Inflation Rate | Rate = ((New CPI - Old CPI) / Old CPI) × 100 | ((110 - 100) / 100) × 100 = 10% | Price level changes |
| ROI | ROI = ((Gain - Cost) / Cost) × 100 | ((500 - 400) / 400) × 100 = 25% | Investment returns |
Special Cases & Edge Cases
🔢 Zero Original Value
When original value = 0
Cannot calculate percentage change
Consider absolute change instead
Use case: New business starting from zero
📈 Negative Original Values
Formula uses absolute value
Ensures positive division
Example: From -100 to -50 = +50% increase
Direction still meaningful
🎯 Very Small Changes
Small absolute changes can be large percentages
Example: $1 increase on $2 item = 50%
Context matters for interpretation
Common Mistakes to Avoid
❌ Wrong Base
Always divide by original value
Not new value or average
Formula: (New - Original) / |Original|
❌ Ignoring Direction
Positive = increase, negative = decrease
Don't just look at magnitude
Sign indicates trend direction
❌ Scale Confusion
Percentage vs absolute values
Use appropriate metric for context
Both can be useful together