What Is Percentage Change?
Percentage increase and decrease both describe how much a value has changed relative to its starting point. This is different from simply knowing the raw difference — it tells you the change in proportion, which is far more meaningful for comparisons.
For example, a price rising by $10 means very different things if the original price was $20 versus $1,000.
The Percentage Change Formula
Both increases and decreases use the same formula:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
- A positive result means an increase.
- A negative result means a decrease.
Step-by-Step: Calculating a Percentage Increase
Suppose a product's price went from $80 to $100. What is the percentage increase?
- Find the difference: $100 − $80 = $20
- Divide by the original value: $20 ÷ $80 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
The price increased by 25%.
Step-by-Step: Calculating a Percentage Decrease
Now suppose that same item goes on sale from $100 back down to $80. What is the percentage decrease?
- Find the difference: $80 − $100 = −$20
- Divide by the original value: −$20 ÷ $100 = −0.20
- Multiply by 100: −0.20 × 100 = −20%
The price decreased by 20%.
Notice: a 25% increase followed by a 20% decrease returns to the same price — they are NOT equal and opposite percentages because the base value changed.
Common Percentage Change Scenarios
| Scenario | Old Value | New Value | % Change |
|---|---|---|---|
| Salary raise | $50,000 | $55,000 | +10% |
| Sale discount | $200 | $150 | −25% |
| Website traffic | 1,200 visits | 1,500 visits | +25% |
| Weight loss | 180 lbs | 162 lbs | −10% |
How to Find the New Value After a Percentage Change
If you know the original value and the percentage change, you can find the new value:
New Value = Old Value × (1 + Percentage Change ÷ 100)
Example: A $60 item increases by 15%.
- New Value = $60 × (1 + 0.15) = $60 × 1.15 = $69
For a decrease, subtract instead: $60 × (1 − 0.15) = $60 × 0.85 = $51
Key Mistakes to Avoid
- Wrong base value: Always divide by the original (old) value, not the new one.
- Confusing raw change with percentage change: A change of 50 units means nothing without the base.
- Assuming symmetry: A 50% increase followed by a 50% decrease does NOT return to the original value.
Summary
Use the formula ((New − Old) ÷ Old) × 100 to find any percentage change. Positive numbers are increases, negative numbers are decreases. Always make sure you're using the correct original value as your denominator.