Formulas
Percentage change = (New − Old) ÷ |Old| × 100
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Example: A price rises from $80 to $100: (100 − 80) ÷ 80 × 100 = 25% increase. If it falls back from $100 to $80, that is (80 − 100) ÷ 100 × 100 = 20% decrease — the base is different. The percentage difference between 80 and 100 is 20 ÷ 90 × 100 = 22.22%.
Where percentage change is used
- Prices and inflation — how much more something costs than last year.
- Salaries — the size of a raise. A raise from $55,000 to $58,000 is 5.45%.
- Investments — return over a period (for multi-year growth, use the CAGR calculator).
- Business metrics — month-over-month revenue, traffic or conversion changes.
Frequently asked questions
What is the formula for percentage change?
Percentage change = (new value − old value) ÷ |old value| × 100. A positive result is an increase and a negative result is a decrease.
What is the difference between percentage change and percentage difference?
Percentage change has a direction — from an old value to a new one. Percentage difference compares two values without a “before” and “after”, dividing the absolute difference by their average. Use it when neither value is the reference, such as comparing two stores’ prices.
Why doesn’t a 50% drop followed by a 50% rise get me back to where I started?
Because each percentage applies to a different base. $100 falls 50% to $50, and a 50% rise on $50 is only $25, giving $75. To recover a 50% loss you need a 100% gain.
What is the difference between percent and percentage points?
If an interest rate rises from 4% to 5%, it increased by 1 percentage point, but by 25 percent (1 ÷ 4). Reporting the change in percentage points avoids confusion.