Percentage Increase & Decrease Formula — Complete Guide
Understanding percentage increase and decrease is essential for business, finance, and everyday life. This guide covers the formulas, step-by-step examples, and common applications.
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The Percentage Change Formulas
↑ Percentage Increase
((New - Original) / Original) × 100
Used when the new value is larger than the original.
↓ Percentage Decrease
((Original - New) / Original) × 100
Used when the new value is smaller than the original.
Universal Formula (handles both)
Percentage Change = ((New Value - Original Value) / Original Value) × 100
A positive result = increase. A negative result = decrease.
Business & Finance Examples
💼 Salary Raise
Your annual salary increased from $52,000 to $58,500. What percentage raise did you receive?
- Change = $58,500 - $52,000 = $6,500
- Percentage = ($6,500 / $52,000) × 100
- = 0.125 × 100 = 12.5% raise
📈 Stock Price Change
A stock dropped from $145.20 to $128.50. What's the percentage decrease?
- Change = $128.50 - $145.20 = -$16.70
- Percentage = (-$16.70 / $145.20) × 100
- = -0.1150 × 100 = -11.5% (decrease)
🏠 Rent Increase
Your monthly rent went from $1,400 to $1,540. What's the percentage increase?
- Change = $1,540 - $1,400 = $140
- Percentage = ($140 / $1,400) × 100
- = 0.10 × 100 = 10% increase
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Applying a Percentage Change
Sometimes you need to calculate the result after applying a percentage change:
After an Increase
New = Original × (1 + %/100)
$200 + 15% = $200 × 1.15 = $230
After a Decrease
New = Original × (1 - %/100)
$200 - 25% = $200 × 0.75 = $150
Common Mistakes to Avoid
- ❌ Using the wrong base: Always divide by the original value, not the new value. A price going from $100 to $150 is a 50% increase, but going from $150 to $100 is only a 33.3% decrease.
- ❌ Assuming symmetry: A 50% increase followed by a 50% decrease does NOT return to the original. $100 → +50% → $150 → -50% → $75 (not $100!).
- ❌ Confusing change with difference: Percentage change has a direction (from old to new). Percentage difference treats both values equally.
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Related Calculators
Frequently Asked Questions
What is the formula for percentage increase?
Percentage Increase = ((New Value - Original Value) / Original Value) × 100. For example, if a price goes from $50 to $65: ((65-50)/50) × 100 = 30% increase.
What is the formula for percentage decrease?
Percentage Decrease = ((Original Value - New Value) / Original Value) × 100. For example, if a price drops from $80 to $60: ((80-60)/80) × 100 = 25% decrease.
How do I calculate a salary raise percentage?
Use the percentage increase formula: ((New Salary - Old Salary) / Old Salary) × 100. If your salary went from $50,000 to $55,000: ((55000-50000)/50000) × 100 = 10% raise.
What is the difference between percentage change and percentage difference?
Percentage change measures increase or decrease from an original value (directional). Percentage difference compares two values without implying one is the original (non-directional). Use change for before/after comparisons; use difference for comparing two independent values.
Can percentage increase be more than 100%?
Yes! A percentage increase over 100% means the value more than doubled. For example, if a stock goes from $10 to $25, that's a 150% increase. A 200% increase means the value tripled.
How do I calculate the new value after a percentage increase?
New Value = Original Value × (1 + Percentage/100). For a 15% increase on $200: $200 × (1 + 15/100) = $200 × 1.15 = $230.