Percentage Change
Calculate the percentage increase or decrease between two numbers.
What is percentage change?
Percentage change measures how much a value has grown or shrunk relative to its starting point, expressed as a percentage. It is one of the most widely used calculations in everyday life — from tracking a salary increase, understanding price inflation, reading financial reports, to interpreting scientific data.
A positive result means the value increased (a percentage increase). A negative result means it decreased (a percentage decrease). The sign and magnitude together give you the full picture of how much has changed and in which direction.
The percentage change formula
The standard formula is:
% Change = ((New Value − Old Value) ÷ |Old Value|) × 100The absolute value of the old number (|Old|) is used in the denominator to handle negative starting values correctly. Without it, a move from −50 to −25 would incorrectly show as a negative change, when in fact the value has improved (become less negative).
Worked examples:
Price rises from $80 to $100:
% change = ((100 − 80) ÷ 80) × 100 = +25%
Headcount falls from 500 to 420:
% change = ((420 − 500) ÷ 500) × 100 = −16%
Temperature drops from −10°C to −4°C:
% change = ((−4 − (−10)) ÷ |−10|) × 100 = +60%Percentage change vs. percentage difference
| Concept | Formula | When to use |
|---|---|---|
| Percentage change | ((New − Old) ÷ |Old|) × 100 | When one value is clearly the "starting point" and the other is the result |
| Percentage difference | (|A − B| ÷ ((A + B) ÷ 2)) × 100 | When neither value is the baseline — comparing two peers |
| Percentage of | (Part ÷ Whole) × 100 | Expressing one number as a share of another |
Common real-world uses
Watch out: the baseline matters enormously
A 50% increase followed by a 50% decrease does not return you to the starting point. Starting at 100, a 50% increase gives 150. A 50% decrease from 150 gives 75 — 25% below the original value. This asymmetry trips up many investors and analysts who assume percentage moves are reversible.
Conversely, a 100% increase doubles a value, while a 50% decrease halves it. To undo a 50% loss, you need a 100% gain. To undo a 10% loss, you need an 11.1% gain. The steeper the loss, the harder the recovery.
Tips for interpreting percentage changes
- Always check the base. A 100% increase sounds impressive. But if the starting value was 1, the new value is only 2. Small absolute numbers can produce large percentages.
- Beware cherry-picked periods. Percentage change depends entirely on the start and end dates. Adjusting the window by a week can turn a gain into a loss. Look for consistent, standardised reporting periods.
- Use CAGR for multi-year growth. If something grew from 100 to 200 over 5 years, the simple percentage change is 100% — but the compound annual growth rate (CAGR) is only 14.9% per year. CAGR is more meaningful for sustained trends.
- Pair with absolute numbers. A 200% revenue increase at a startup might be $200K. A 5% increase at a large retailer might be $500M. Always pair percentage change with the actual numbers to understand scale.
Calculates the percentage increase or decrease from an original value to a new value. Used for price changes, growth rates, performance changes and more.
% change = ((New − Old) ÷ |Old|) × 100