How to Calculate Percentage Increase and Decrease
Use the percentage change formula, examples, and calculator
Percentage Change Formula
To calculate percentage increase or decrease, subtract the old value from the new value, divide by the old value, then multiply by 100.
A positive result is a percentage increase. A negative result is a percentage decrease. For example, going from 50 to 60 is ((60 - 50) / 50) x 100 = 20% increase.
Calculate Percentage Change
Percentage Calculator
Choose a calculation type, fill in the values, and click Calculate.
What is X% of a number?
%
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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.