Percentage Change Calculator
Free percentage change calculator. Find the percent change between two numbers. Calculate growth rates, price changes, and performance differences instantly.
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Understanding results
The calculator provides:
- Percentage Change: The relative change expressed as a percentage (positive for increase, negative for decrease)
- Direction: Whether the change was an increase or decrease
- Absolute Change: The actual numeric difference between the two values
Positive percentage change means growth; negative means decline.
Purpose
The percentage change calculator determines the relative change between two values, expressed as a percentage. Whether you're tracking stock performance, comparing prices over time, analyzing sales growth, or measuring any kind of change, this tool provides instant, accurate results.
Percentage change is one of the most commonly used metrics in business, finance, science, and everyday life. It helps you understand the magnitude and direction (increase or decrease) of change between any two values.
How to use
Using the percentage change calculator:
- Enter the Old Value: Input the original or starting value (the "from" value).
- Enter the New Value: Input the new or ending value (the "to" value).
- View Results: The calculator shows the percentage change, whether it's an increase or decrease, and the absolute change amount.
Examples
Example 1: Stock Performance
A stock went from $120 to $156 over a year.
- Percentage Change = (($156 - $120) / $120) × 100 = 30% increase
Example 2: Price Comparison
Gas prices went from $3.50 to $3.15 per gallon.
- Percentage Change = (($3.15 - $3.50) / $3.50) × 100 = -10% (10% decrease)
Example 3: Sales Growth
Quarterly sales went from $50,000 to $62,500.
- Percentage Change = (($62,500 - $50,000) / $50,000) × 100 = 25% increase
Example 4: Population Change
A city's population went from 100,000 to 85,000.
- Percentage Change = ((85,000 - 100,000) / 100,000) × 100 = -15% (15% decrease)
How it works
Formula: Percentage Change = ((New - Old) / |Old|) × 100
- Find the difference: Subtract the old value from the new value
- Divide by the original: Divide by the absolute value of the old value
- Convert to percentage: Multiply by 100
Example: Change from 80 to 100
- Difference: 100 - 80 = 20
- Divide: 20 / 80 = 0.25
- Convert: 0.25 × 100 = 25% increase
FAQ
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Formula: ((New - Old) / Old) × 100. A positive result is an increase; negative is a decrease.
What is the percentage change from 50 to 75?
Percentage Change = ((75 - 50) / 50) × 100 = 50% increase.
What is the difference between percentage change and percentage difference?
Percentage change measures change from an original value to a new value (has direction - increase or decrease). Percentage difference measures how far apart two values are relative to their average (no direction, always positive).
Can percentage change be negative?
Yes, a negative percentage change indicates a decrease. For example, if a price drops from $100 to $80, the percentage change is -20%, meaning a 20% decrease.
What if the old value is zero?
Percentage change is undefined when the old value is zero (division by zero). In such cases, you may need to use a different metric or consider the change as going from nothing to something.
Methodology
The percentage change formula is:
Percentage Change = ((New Value - Old Value) / |Old Value|) × 100
Where:
- A positive result indicates an increase
- A negative result indicates a decrease
Example Calculation
Stock price changed from $50 to $65:
- Change = $65 - $50 = $15
- Percentage Change = ($15 / $50) × 100 = 30% increase
Stock price changed from $50 to $40:
- Change = $40 - $50 = -$10
- Percentage Change = (-$10 / $50) × 100 = -20% (20% decrease)
Validation & Accuracy
Tested: Verified against financial calculators and spreadsheet functions.
Accuracy: Results are exact, rounded to 2 decimal places for display.
Sources
Based on standard mathematical and financial formulas for percentage change calculations, used globally in business, economics, and science.