How to Calculate Percentage Increase or Decrease
The percentage change calculator helps you find how much a value has increased or decreased relative to its original amount. It's essential for tracking price changes, analyzing growth rates, measuring performance improvements, and understanding financial data.
What Is Percentage Change?
Percentage change measures how much a quantity has changed relative to its original value, expressed as a percentage. A positive result indicates an increase, while a negative result indicates a decrease. It's different from the absolute change (the raw difference) because it shows the change in relative terms.
The Formula
Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100. Subtract the old from the new, divide by the old, then multiply by 100.
Example:
If a stock price rises from $80 to $100: ((100 - 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase.
Common Use Cases
Real-world applications for this calculator
Price Changes
Track how much prices have risen or fallen. If gas went from $3.50 to $4.20 per gallon: ((4.20 - 3.50) ÷ 3.50) × 100 = 20% increase.
Investment Returns
Calculate investment performance. If your portfolio grew from $10,000 to $12,500: ((12500 - 10000) ÷ 10000) × 100 = 25% return.
Sales Performance
Measure sales growth or decline. If monthly sales went from 500 to 650 units: ((650 - 500) ÷ 500) × 100 = 30% increase.
Population Growth
Analyze demographic changes. If a city's population grew from 50,000 to 58,000: ((58000 - 50000) ÷ 50000) × 100 = 16% growth.
Tips
- Always use the original (starting) value as the denominator.
- Negative results indicate a decrease; positive results indicate an increase.
- Percentage changes are not symmetrical-a 25% increase followed by a 25% decrease does not return to the original value.
- For comparing periods, ensure you're using consistent time frames.
Frequently Asked Questions
How do I calculate percentage change?
Subtract the original value from the new value, divide by the original value, and multiply by 100. Formula: ((New - Original) ÷ Original) × 100. A positive result is an increase; negative is a decrease.
What is the percentage change from 100 to 150?
The percentage change from 100 to 150 is a 50% increase. Calculate: ((150 - 100) ÷ 100) × 100 = 50%.
What is the difference between percentage change and percentage points?
Percentage change is relative to the original value, while percentage points measure the absolute difference between two percentages. For example, going from 40% to 50% is a 10 percentage point increase, but a 25% relative increase ((50-40)/40 × 100).
Why isn't a 50% increase followed by a 50% decrease equal to the original?
Because the decrease is calculated from the new (higher) value. If 100 increases by 50%, it becomes 150. A 50% decrease from 150 is 75, leaving you at 75-not 100. Percentage changes are not symmetrical.
How do I calculate percentage decrease?
Use the same formula: ((New - Original) ÷ Original) × 100. If the new value is smaller, you'll get a negative result indicating a decrease. For example, from 200 to 150: ((150 - 200) ÷ 200) × 100 = -25%.