How to Calculate Percentage Increase and Decrease
Essential skill for shopping, investing, and everyday life
Why This Matters
Every day you encounter percentage changes:
- "50% off sale!"
- "Stock market up 3% today"
- "Rent increased by 5%"
- "Lost 10% body weight"
Understanding percentage change helps you make better decisions with money, health, and investments.
Percentage Increase Formula
Percentage Decrease Formula
Both formulas are the same! Decrease will give a negative number.
Step-by-Step Examples
Example 1: Salary Raise (Increase)
Problem: Your salary went from $50,000 to $55,000. What's the percentage increase?
Solution:
- Find the difference: $55,000 - $50,000 = $5,000
- Divide by original: $5,000 / $50,000 = 0.10
- Multiply by 100: 0.10 × 100 = 10% increase
Example 2: Sale Discount (Decrease)
Problem: A $80 jacket is now $60. What's the percentage decrease?
Solution:
- Find the difference: $80 - $60 = $20
- Divide by original: $20 / $80 = 0.25
- Multiply by 100: 0.25 × 100 = 25% decrease
Example 3: Stock Market Change
Problem: Stock price went from $150 to $165. What's the change?
Solution:
- Difference: $165 - $150 = $15
- Divide: $15 / $150 = 0.10
- Result: 10% increase
🧮 Calculate Any Percentage Change
Let our calculator do the math for you - just enter the old and new values!
Open Percentage Calculator →Common Real-World Scenarios
1. Price Increases
| Item | Old Price | New Price | % Change |
|---|---|---|---|
| Gas | $3.00/gal | $3.60/gal | +20% |
| Rent | $1,200/mo | $1,320/mo | +10% |
| Groceries | $150/wk | $165/wk | +10% |
2. Sale Discounts
| Item | Original | Sale Price | % Off |
|---|---|---|---|
| TV | $500 | $400 | 20% off |
| Shoes | $100 | $70 | 30% off |
| Laptop | $1,000 | $850 | 15% off |
Quick Mental Math Tricks
10% Rule
To find 10% increase or decrease:
- Increase: Add 10% to original (Original × 1.10)
- Decrease: Subtract 10% (Original × 0.90)
Example: 10% off $80 = $80 × 0.90 = $72
50% Rule (Half)
50% decrease means half the original price.
Example: 50% off $60 = $30
Double = 100% Increase
If something doubles, that's a 100% increase.
Example: $50 → $100 = 100% increase
Common Mistakes to Avoid
❌ Mistake 1: Using the wrong base
Always divide by the ORIGINAL (old) value, not the new value.
Wrong: ($60 - $50) / $60 = 16.7%
✅ Right: ($60 - $50) / $50 = 20%
❌ Mistake 2: Confusing % and percentage points
If interest goes from 5% to 8%:
- Change = 3 percentage points
- Increase = (3/5) × 100 = 60% increase
Reverse Calculations
Find Original Price After Discount
Problem: Item costs $80 after 20% discount. What was original price?
Solution:
- $80 represents 80% of original (100% - 20% = 80%)
- Original = $80 / 0.80 = $100
Find New Price After Increase
Problem: $200 item increased by 15%. What's the new price?
Solution:
- New = $200 × 1.15 = $230
Practice Problems
- Population grew from 10,000 to 12,500. What's the % increase?
- Weight dropped from 180 lbs to 162 lbs. What's the % decrease?
- Investment rose from $5,000 to $6,250. What's the % gain?
Answers: 1) 25%, 2) 10%, 3) 25%
Frequently Asked Questions
Can percentage change be over 100%?
Yes! If something triples, that's a 200% increase. If it quadruples, that's 300%.
How do I calculate multiple percentage changes?
Multiply the multipliers: Price up 20% then down 10% = 1.20 × 0.90 = 1.08 = 8% net increase.
What if I get a negative number?
Negative = decrease, Positive = increase. The sign tells you the direction of change.