Percentage Change Calculator
Calculate percentage change, increase, decrease, and find original values before percentage changes.
Percentage Change from A to B
Enter Your Values
Enter old and new values to calculate the percentage change between them.
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About This Calculator
Understanding percentage change is essential for making sense of the numbers that shape our daily lives. Whether you're tracking your investment portfolio's performance, calculating salary increases, measuring business growth, or simply figuring out how much you'll save during a sale, percentage change calculations are everywhere.
Percentage change tells you how much a value has increased or decreased relative to its original amount, expressed as a percentage. This standardized measurement allows you to compare changes across different scales and contexts. A $10 increase might seem small, but if it represents a 50% gain on a $20 investment, that's significant. Conversely, a $1,000 increase on a $100,000 investment is only 1%.
Our comprehensive Percentage Change Calculator handles five essential calculation types: computing percentage change between two values, adding a percentage to a number (useful for tax and tip calculations), subtracting a percentage (perfect for discounts and markdowns), finding the original value before a percentage change, and calculating the percentage difference between two values. Each mode displays the formula used and provides step-by-step calculations so you understand exactly how the result was derived.
The visual indicators make it easy to see at a glance whether you're dealing with an increase (shown in green) or a decrease (shown in red). This intuitive color-coding helps you quickly interpret results, especially when working with multiple calculations in financial planning, academic research, or business analysis.
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How to Use the Percentage Change Calculator
- 1**Select your calculation type**: Choose from five modes - Percentage Change (A to B), Add Percentage, Subtract Percentage, Find Original Value, or Percentage Difference.
- 2**Enter your values**: Input the required numbers based on your selected mode. For percentage change, enter the old and new values. For increase/decrease, enter the base value and percentage.
- 3**Click Calculate**: The calculator will compute your result instantly, showing the answer with appropriate color coding (green for increase, red for decrease).
- 4**Review the formula**: See exactly which mathematical formula was applied to your calculation for verification and learning.
- 5**Follow the step-by-step breakdown**: Each calculation shows detailed steps so you can understand and replicate the math manually if needed.
- 6**Use visual indicators**: For percentage change calculations, the visual comparison helps you understand the magnitude of the change at a glance.
- 7**Share or print your results**: Use the share button to copy a link with your calculation, or print the results for documentation.
Formula
Percentage Change = ((New Value - Old Value) / |Old Value|) x 100The percentage change formula measures relative change by dividing the absolute change by the original value and multiplying by 100. Positive results indicate increase, negative results indicate decrease. For percentage difference between two values with no clear 'original,' use the average as the denominator instead.
The Percentage Change Formula Explained
The percentage change formula is one of the most useful mathematical tools for everyday life:
Percentage Change = ((New Value - Old Value) / |Old Value|) x 100
Let's break this down:
- Subtract the old value from the new value to find the difference
- Divide by the absolute value of the old value (original amount)
- Multiply by 100 to convert to a percentage
Example: A stock price goes from $50 to $65
- Difference: $65 - $50 = $15
- Divide by original: $15 / $50 = 0.30
- Convert to percentage: 0.30 x 100 = 30%
- Result: 30% increase
Why use absolute value? When the original value is negative (like a loss turning into a gain), using the absolute value ensures the percentage makes sense contextually.
Percentage Increase vs. Decrease
Understanding the difference between percentage increase and decrease is crucial for accurate calculations:
Percentage Increase (Adding X%) When adding a percentage to a value:
- Formula: New Value = Original x (1 + Percentage/100)
- Example: $100 + 20% = $100 x 1.20 = $120
- The increase amount itself is: $100 x 0.20 = $20
Percentage Decrease (Subtracting X%) When subtracting a percentage from a value:
- Formula: New Value = Original x (1 - Percentage/100)
- Example: $100 - 20% = $100 x 0.80 = $80
- The decrease amount itself is: $100 x 0.20 = $20
Key Insight: A 20% increase followed by a 20% decrease does NOT return you to the original value!
- Start: $100
- After 20% increase: $120
- After 20% decrease: $120 x 0.80 = $96
- You've lost $4 overall!
This asymmetry is why investors who lose 50% need a 100% gain just to break even.
Finding the Original Value (Reverse Percentage)
Sometimes you know the final value and the percentage change, but need to find the original. This is called reverse percentage calculation.
After a Percentage Increase: Original = Final Value / (1 + Percentage/100)
Example: A price after 25% markup is $125. What was the original?
- Original = $125 / 1.25 = $100
After a Percentage Decrease: Original = Final Value / (1 - Percentage/100)
Example: A sale price after 30% off is $70. What was the original?
- Original = $70 / 0.70 = $100
Common Mistake: Don't simply reverse the percentage!
- Wrong: $70 + 30% = $91 (incorrect!)
- Right: $70 / 0.70 = $100 (correct!)
This calculation is essential for:
- Finding pre-sale prices
- Calculating pre-tax amounts
- Determining original values before inflation adjustments
Common Applications in Finance and Business
Percentage change calculations are fundamental to financial analysis:
Investment Returns
- Calculate portfolio performance over time
- Compare returns across different investment types
- Measure annual growth rates (CAGR requires sequential percentage changes)
Stock Market Analysis
- Daily/weekly/monthly price changes
- Year-over-year (YoY) comparisons
- Earnings growth calculations
Business Metrics
- Revenue growth or decline
- Customer acquisition cost changes
- Profit margin analysis
- Market share shifts
Personal Finance
- Salary increase calculations
- Inflation impact on purchasing power
- Loan interest rate comparisons
- Savings growth tracking
Retail and Sales
- Discount calculations for shoppers
- Markup calculations for retailers
- Same-store sales comparisons
- Year-over-year sales performance
Percentage Difference vs. Percentage Change
These two concepts are often confused but serve different purposes:
Percentage Change measures how much a value has changed relative to its starting point:
- Has a direction (positive for increase, negative for decrease)
- Uses the original value as the reference point
- Formula: ((New - Old) / |Old|) x 100
Percentage Difference measures how different two values are relative to their average:
- No direction - always positive (uses absolute difference)
- Uses the average of both values as reference
- Formula: (|Value1 - Value2| / ((Value1 + Value2) / 2)) x 100
When to use each:
Use Percentage Change when:
- Tracking changes over time (before/after)
- One value is clearly the 'original' or 'baseline'
- Direction of change matters
Use Percentage Difference when:
- Comparing two independent measurements
- Neither value is a 'starting point'
- Comparing experimental results or survey responses
Everyday Applications: Sales, Inflation, and More
Shopping and Sales Understanding percentage changes helps you become a smarter shopper:
- A '50% off' sale means you pay half the original price
- Successive discounts: 20% off then 10% off does NOT equal 30% off
- $100 with 20% off = $80, then 10% off = $72 (28% total discount)
- 'Buy one get one 50% off' is effectively a 25% discount on two items
Inflation and Cost of Living
- If inflation is 3%, prices increase by 3% annually
- To maintain purchasing power, income must grow by at least the inflation rate
- Real wage growth = Nominal wage increase - Inflation rate
Salary and Compensation
- A 5% raise on $50,000 adds $2,500 annually
- Compare job offers by calculating total compensation percentage differences
- Negotiation tip: Know the percentage increase you're requesting, not just the dollar amount
Health and Fitness
- Weight loss/gain as percentage of body weight
- Performance improvement in exercise metrics
- Medication dosage changes
Pro Tips
- 💡For quick mental math, remember that 10% is just moving the decimal point one place left. So 10% of $85 is $8.50, and 20% is double that: $17.
- 💡When comparing percentage changes, always check the base values. A 10% increase from $1,000 is much larger ($100) than a 10% increase from $100 ($10).
- 💡To find what percentage one number is of another, divide the part by the whole and multiply by 100. For example, 25 is what percent of 200? (25/200) x 100 = 12.5%.
- 💡Remember the rule of 72: divide 72 by the annual growth rate to estimate how many years it takes for an investment to double. At 8% growth, doubling takes about 9 years.
- 💡When negotiating salary, know both the percentage and dollar amount. A 5% raise sounds modest, but on a $100,000 salary, that's $5,000 extra per year.
- 💡Successive percentage decreases compound negatively. A 20% loss followed by another 20% loss isn't a 40% total loss - it's actually a 36% total loss (0.80 x 0.80 = 0.64).
- 💡For sales shopping, calculate the final price quickly: for 30% off, just multiply by 0.70. For 25% off, multiply by 0.75 (or divide by 4, multiply by 3).
- 💡When tracking weight loss, use percentages rather than pounds for more meaningful comparisons. Losing 10% of body weight is significant regardless of starting weight.
- 💡Interest rates and percentage changes on percentages can be confusing. A rate going from 2% to 3% is a 1 percentage point increase, but a 50% relative increase.
- 💡Always clarify 'percent of' vs 'percent off' in sales contexts. '25% of the price' means you pay 25%, while '25% off the price' means you pay 75%.
- 💡For investment returns, time matters. A 100% return over 10 years is about 7.2% annually compounded, which is very different from 10% simple annual returns.
- 💡When comparing statistics, consider whether percentage change or absolute numbers tell the better story. A 100% increase in rare events might still be insignificant in absolute terms.
Frequently Asked Questions
To calculate percentage change, subtract the old value from the new value, divide by the absolute value of the old value, then multiply by 100. The formula is: ((New Value - Old Value) / |Old Value|) x 100. For example, if a price goes from $80 to $100, the calculation is: (($100 - $80) / $80) x 100 = 25% increase. A positive result indicates an increase, while a negative result indicates a decrease.