Education
Percentage Increase and Decrease Explained
Learn to calculate percentage changes, growth rates, and understand increases vs decreases.
- 6 min read
Formula
New Value = Original × (1 + Percentage ÷ 100)
Percentage Increase = ((New - Original) ÷ Original) × 100
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Understanding Percentage Change
Percentage change measures how much a value has increased or decreased relative to its original amount. It is essential for understanding growth rates, price changes, and comparing data over time.
Percentage Increase Formula
Percentage Increase = ((New - Original) ÷ Original) × 100
Example: Price Increase
A product was $50 and now costs $60:
- Difference: $60 - $50 = $10
- Divide by original: $10 ÷ $50 = 0.20
- Multiply by 100: 0.20 × 100 = 20%
- Result: 20% increase
Percentage Decrease Formula
Percentage Decrease = ((Original - New) ÷ Original) × 100
Example: Price Decrease
A product was $80 and now costs $60:
- Difference: $80 - $60 = $20
- Divide by original: $20 ÷ $80 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
- Result: 25% decrease
Important Concept: It's Not Symmetrical!
A 50% increase followed by a 50% decrease does NOT return to the original value!
Example:
- Start: $100
- Increase 50%: $100 × 1.50 = $150
- Decrease 50%: $150 × 0.50 = $75
- You end up with $75, not $100!
Percentage Points vs Percentage Change
These are different concepts:
- Percentage Points: Absolute difference between two percentages
- Percentage Change: Relative change from original to new
Example:
If interest rate goes from 4% to 6%:
- Percentage point increase: 6% - 4% = 2 percentage points
- Percentage increase: (6 - 4) ÷ 4 × 100 = 50% increase
Real-World Applications
| Application | What It Measures |
|---|---|
| Stock prices | Daily/yearly returns |
| Sales growth | Revenue changes |
| Population | Growth/decline rates |
| Inflation | Price level changes |
| Weight loss | Body weight changes |
Frequently Asked Questions
How do I calculate a percentage increase?
Subtract the original from the new value, divide by the original and multiply by 100: from $50 to $60 is 10 ÷ 50 × 100 = 20%.
How do I calculate a percentage decrease?
Subtract the new value from the original, divide by the original and multiply by 100: from $80 to $60 is 20 ÷ 80 × 100 = 25%.
Why doesn't a 50% increase cancel out a 50% decrease?
Because each change is measured from a different base. $100 up 50% is $150; $150 down 50% is $75, not $100. To undo a 50% increase you need a 33.3% decrease.