Percentage Change Calculator
Calculate the percentage increase or decrease between any two values. Useful for tracking price changes, growth rates, and statistics.
Percentage Change Formula
The percentage change formula measures how much a value has grown or shrunk relative to its starting point: % Change = ((New − Original) / |Original|) × 100. A positive result is an increase; a negative result is a decrease. The absolute value of the original is used in the denominator to handle negative starting values correctly.
Percentage change is used everywhere: stock returns, inflation rates, revenue growth, population change, test score improvements, and price comparisons. Understanding how to calculate and interpret it correctly is a fundamental quantitative skill.
Real-World Percentage Change Examples
| Scenario | Original | New Value | Change |
|---|---|---|---|
| Stock gain | $100 | $135 | +35% |
| Salary raise | $50,000 | $55,000 | +10% |
| Price drop (sale) | $80 | $60 | −25% |
| Revenue growth | $1M | $1.4M | +40% |
| Population decline | 10,000 | 8,500 | −15% |
| Inflation | $3.50 (gas) | $4.20 (gas) | +20% |
Percentage Increase vs. Percentage Decrease
Percentage increases and decreases are not symmetric. A 20% increase followed by a 20% decrease results in a net loss of 4%, not zero. Starting at 100: after +20% = 120, after −20% of 120 = 96. To reverse a given percentage increase, you need a smaller percentage decrease, and vice versa.
This asymmetry is why financial advisors emphasize capital preservation. A 50% portfolio loss requires a 100% gain to recover. A 10% loss requires only an 11.1% gain. The math becomes increasingly unfavorable as losses grow, which is why risk management in investing focuses heavily on avoiding large drawdowns.
Frequently Asked Questions
What is the percentage change formula?
Percentage Change = ((New Value − Original Value) / |Original Value|) × 100. The absolute value of the original is used so the formula works correctly with negative starting values. A positive result means increase; negative means decrease. Example: original = 80, new = 100. Change = (100 − 80) / 80 × 100 = +25%. Going from 100 to 80: (80 − 100) / 100 × 100 = −20%. Note that a 25% increase followed by a 20% decrease does NOT return to the original — a common misconception.
What is the difference between percentage change and percentage points?
Percentage change measures the relative change between two values using the formula above. Percentage points measure the absolute arithmetic difference between two percentages. Example: interest rate rises from 4% to 6%. Percentage point change = 6 − 4 = 2 percentage points. Percentage change = (6 − 4) / 4 × 100 = 50% increase. These are very different numbers. Misusing percentage points vs. percentage change is one of the most common mathematical errors in news media and business reporting.
How do I calculate a percentage increase in price?
Use the standard formula: ((New Price − Old Price) / Old Price) × 100. Example: a product rises from $45 to $54. Increase = ($54 − $45) / $45 × 100 = $9 / $45 × 100 = 20% increase. To reverse this — if you know a price increased by 20% and the new price is $54, the original was $54 / 1.20 = $45. This reverse calculation is useful when you know only the final price and the rate of increase.
Why does a 50% increase followed by a 50% decrease not return to the original?
Because percentage changes are calculated on different bases. Start at 100. A 50% increase gives 150. A 50% decrease from 150 gives 75 — not 100. The asymmetry is fundamental to percentage math. To return to the original from a 50% increase, you would need a 33.3% decrease (since 150 × 0.667 ≈ 100). This is why investment losses require larger percentage gains to recover: a 50% loss requires a 100% gain to get back to even.