Percentage Change – One Formula for Everything
Percentage change is a single formula that covers both increases and decreases. It tells you how large a change is relative to the starting value, making it the standard way to compare changes across different situations.
This single signed formula unifies everything covered elsewhere in this category — percentage increase, decrease, profit, loss, discount, and markup are all just percentage change applied to a specific context, with the sign telling you which direction the value moved. Financial news reports rely on this constantly: a stock market index reported as "down 2.3% today" or a currency exchange rate "up 0.8% this week" are both instances of the exact same formula, just with the everyday interpretation of the sign built into the wording.
The Formula
Percentage Change = ((New Value minus Original Value) / Original Value) times 100. A positive result is an increase; a negative result is a decrease.
Worked Examples
Change = 250 - 200 = 50. (50 / 200) times 100 = +25% (increase).
Change = 15 - 20 = -5. (-5 / 20) times 100 = -25% (decrease).
(26400 - 24000) / 24000 times 100 = 2400/24000 times 100 = +10%.
(64 - 80) / 80 times 100 = -16/80 times 100 = -20%.
Finding a New Value from a Percentage Change
| Change | Multiplier | Example |
|---|---|---|
| +15% | 1.15 | 300 times 1.15 = 345 |
| -20% | 0.80 | 500 times 0.80 = 400 |
| +100% | 2.00 | Value doubles |
| -50% | 0.50 | Value halves |
Successive Percentage Changes
When multiple percentage changes happen one after another, multiply the multipliers together.
Combined multiplier = 1.20 times 0.90 = 1.08. Net effect: +8% increase. (Not 10% — order and multiplication matter.)
Combined multiplier = 1.05 times 1.05 times 1.05 = 1.1576. Net effect: +15.76%.
Common Mistakes
- Dividing by the new value instead of the original — always use the original as the denominator.
- Adding successive percentages: a 20% rise followed by a 20% fall does NOT return to the original value.
- Confusing the result of a percentage change with the percentage itself.
Key Takeaways
- Percentage change = (change / original) times 100. Positive means increase; negative means decrease.
- Always divide by the original (starting) value.
- For successive changes, multiply the multipliers, not the percentages.
- A 50% increase followed by a 50% decrease does not return to the start: 100 times 1.5 times 0.5 = 75.