Seeing percentage change in action helps build understanding. Below are four real-world examples showing how to calculate percentage change step by step, including increases, decreases, and edge cases. Work through each one to strengthen your grasp of the concept, then use our percentage change calculator to verify your own calculations.
Example 1: Percentage increase
Real-world scenario: You received a salary raise. Your old salary was $40,000 per year, and your new salary is $48,000 per year. What's your percentage raise?
1Identify your values
Original value (old salary): $40,000
New value (new salary): $48,000
2Find the difference
New value − Original value
$48,000 − $40,000 = $8,000
3Divide by the original value
$8,000 ÷ $40,000 = 0.20
4Multiply by 100
0.20 × 100 = 20%
5Add the sign and context
Your salary increased by 20% ✓
Formula shown:
(48,000 − 40,000) ÷ 40,000 × 100 = 20%
Example 2: Percentage decrease
Real-world scenario: A store is having a sale. A jacket originally priced at $100 is now on sale for $75. What's the discount percentage?
1Identify your values
Original value (original price): $100
New value (sale price): $75
2Find the difference
Original value − New value
$100 − $75 = $25
3Divide by the original value
$25 ÷ $100 = 0.25
4Multiply by 100
0.25 × 100 = 25%
5Add the context
The jacket has a 25% discount ✓
Formula shown:
(100 − 75) ÷ 100 × 100 = 25%
This example shows a percentage decrease in action. The larger the reduction from the original price, the bigger the discount percentage.
Example 3: Negative percentage change
Real-world scenario: A company's revenue dropped. Last quarter they made $500,000 in revenue. This quarter they made $450,000. What's the percentage change?
1Identify your values
Original value (last quarter): $500,000
New value (this quarter): $450,000
2Find the difference
New value − Original value
$450,000 − $500,000 = −$50,000
(Notice it's negative because the new value is smaller)
3Divide by the original value
−$50,000 ÷ $500,000 = −0.10
4Multiply by 100
−0.10 × 100 = −10%
5Interpret the negative sign
Revenue decreased by 10% (or: −10% change) ✓
The negative sign tells us this is a decline, not growth. When calculating percentage increases, you'd see a positive result instead.
Formula shown:
(450,000 − 500,000) ÷ 500,000 × 100 = −10%
Example 4: No change or zero result
Real-world scenario: A stock price was $50 per share. After a week, it's still $50 per share. What's the percentage change?
1Identify your values
Original value (starting price): $50
New value (current price): $50
2Find the difference
New value − Original value
$50 − $50 = $0
3Divide by the original value
$0 ÷ $50 = 0
4Multiply by 100
0 × 100 = 0%
5Interpret the result
The stock price had 0% change (no change) ✓
This is a perfectly valid result—it means the values are identical.
Formula shown:
(50 − 50) ÷ 50 × 100 = 0%
Common percentage change mistakes
❌ Mistake 1: Dividing by the wrong value
You must divide by the original value, not the new value. If a price goes from $100 to $150, the increase is (150 − 100) ÷ 100 × 100 = 50%, NOT (150 − 100) ÷ 150 × 100 = 33.33%.
❌ Mistake 2: Forgetting to multiply by 100
If you stop after dividing by the original value, you'll get a decimal (like 0.25) instead of a percentage (25%). Always multiply by 100 to convert to a percentage.
❌ Mistake 3: Misinterpreting the negative sign
A negative percentage change (like −15%) doesn't mean the answer is wrong—it means the value decreased. Don't add a negative sign to a positive result; the sign tells you the direction of change.
❌ Mistake 4: Assuming the percentages are reversible
A +50% increase followed by a −50% decrease does not return you to the original value. If you start with $100, increase by 50% ($150), then decrease by 50% ($75), you end up with $75, not $100.
❌ Mistake 5: Using percentage change for zero original values
If the original value is zero, percentage change is undefined (division by zero). In this case, describe the change in absolute terms instead.
Try the percentage change calculator
Now that you've seen how percentage change works in different scenarios, test your understanding with our calculator. Enter any two values and watch the calculation work through—it's a great way to reinforce what you've learned.
Use the Calculator