Percentage change is one of the most commonly used calculations in business, finance, and everyday life — and one of the most frequently done incorrectly. Whether you are calculating a raise, a price increase, year-over-year growth, or a discount, the formula is the same.
The Formula
Percentage Change = ((New Value − Old Value) / Old Value) × 100 A positive result means increase; a negative result means decrease. Always divide by the original (old) value.
Examples
| Scenario | Old | New | Calculation | Result |
|---|---|---|---|---|
| Salary raise | $50,000 | $55,000 | (55,000 − 50,000) / 50,000 × 100 | +10% |
| Stock decline | $150 | $120 | (120 − 150) / 150 × 100 | −20% |
| Price increase | $4.50 | $5.25 | (5.25 − 4.50) / 4.50 × 100 | +16.7% |
| Weight loss | 200 lbs | 180 lbs | (180 − 200) / 200 × 100 | −10% |
The #1 Mistake: Percentage Increase ≠ Percentage Decrease
This is where most people get confused. If a stock drops 50% from $100 to $50, it needs to increase 100% (not 50%) to get back to $100. This asymmetry catches even experienced professionals off guard:
- A 10% drop followed by a 10% gain leaves you at 99%, not 100%.
- A 20% drop requires a 25% gain to recover.
- A 33% drop requires a 50% gain to recover.
- A 50% drop requires a 100% gain to recover.
This is because the base changes after each calculation. The decrease is calculated on a larger number; the recovery is calculated on the smaller remaining amount.
Percentage Points vs Percentages
Another common confusion: if an interest rate goes from 5% to 7%, that is a 2 percentage point increase but a 40% increase. "Percentage points" measure the absolute difference between two percentages; "percent change" measures the relative change. In headlines, this distinction matters enormously.
Calculate any percentage operation instantly with the Percentage Calculator.
Key Takeaways
- Always divide by the original value — this is the most common source of errors.
- Percentage drops and gains are not symmetric — a 50% drop requires a 100% gain to recover.
- Percentage points ≠ percent — a rate going from 5% to 7% is a 2 percentage point increase but a 40% relative increase.
- For consecutive changes, multiply the factors: a 10% increase then a 10% decrease is 1.10 × 0.90 = 0.99, or a net 1% loss.
Frequently Asked Questions
How do I calculate percentage increase?
Use the formula: ((New Value - Old Value) / Old Value) x 100. For example, if your salary went from $50,000 to $57,500, the increase is ((57,500 - 50,000) / 50,000) x 100 = 15%. The key is always dividing by the original (old) value.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, 35 is what percent of 200? Answer: (35 / 200) x 100 = 17.5%. You can also reverse this: what is 17.5% of 200? Answer: 200 x 0.175 = 35.
How do I calculate reverse percentage (find the original price)?
If something costs $80 after a 20% discount, the original price is $80 / (1 - 0.20) = $80 / 0.80 = $100. For a price after increase: if something costs $120 after a 20% markup, the original is $120 / 1.20 = $100.