Percentage Increase vs Percentage Decrease: Differences & Formulas

One of the most frequent mathematical misconceptions involves the symmetry of percentages. If an asset decreases in value by 50%, it does not take a 50% gain to recover. It takes a 100% gain. Consider an investment of $100. A 50% loss reduces the value to $50. If that $50 then gains 50% ($25), you only have $75. To return to $100, the $50 balance must double—requiring a full 100% gain.

$$\text{Percentage Increase} = \left(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}}\right) \times 100$$ Example: If a company’s revenue grows from $80,000 to $100,000: $$\left(\frac{100,000 - 80,000}{80,000}\right) \times 100 = \left(\frac{20,000}{80,000}\right) \times 100 = 25\% \text{ increase}$$

$$\text{Percentage Decrease} = \left(\frac{\text{Original Value} - \text{New Value}}{\text{Original Value}}\right) \times 100$$ Example: If retail inventory is marked down from $120 to $90: $$\left(\frac{120 - 90}{120}\right) \times 100 = \left(\frac{30}{120}\right) \times 100 = 25\% \text{ markdown}$$