Formulas
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
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.
How to use the calculator
- Enter the original (old) value and the new value.
- Read the percentage increase or decrease, the absolute change and the percentage difference between the two numbers.
Gains and losses aren’t symmetric
| Change | Percentage change | Change needed to return |
|---|---|---|
| 50 → 75 | +50.0% | -33.3% |
| 80 → 100 | +25.0% | -20.0% |
| 100 → 80 | -20.0% | +25.0% |
| 100 → 150 | +50.0% | -33.3% |
| 200 → 150 | -25.0% | +33.3% |
| 40 → 20 | -50.0% | +100.0% |
Because each percentage is measured against a different starting value, a loss needs a bigger gain to recover. A 50% fall requires a 100% rise to get back to where you started — an important point for investors.
Percentage change vs. percentage points
When the values are already percentages, be careful with wording. If an interest rate rises from 4% to 5%, it has increased by 1 percentage point, but by 25 percent (1 ÷ 4). News reports sometimes mix these up, which can make changes sound much larger or smaller than they are.
Percentage difference
When neither value is the “original” — for example comparing two prices from different stores — use the percentage difference: the absolute difference divided by the average of the two values. For 80 and 100: 20 ÷ 90 = 22.2%. It gives the same answer whichever way round you enter the numbers.
Combining several changes
Successive percentage changes multiply rather than add. A 10% rise followed by a 10% fall leaves you at 1.10 × 0.90 = 0.99, a 1% loss overall. Three yearly increases of 5%, 8% and −3% give 1.05 × 1.08 × 0.97 = 1.100, a total rise of 10.0%. To express a multi-year change as a yearly rate, use the CAGR calculator.
Common uses
- Price changes and discounts, salary raises and inflation.
- Investment returns and portfolio performance.
- Business metrics: month-over-month revenue, traffic or conversion rates.
- Body weight, test scores and other progress tracking.