What Is Percentage Change?
Percentage change measures how much a value has increased or decreased relative to its original value, expressed as a percentage. It is one of the most useful calculations in finance, economics, investing, statistics, and everyday life. Whether you are tracking stock prices, measuring sales growth, comparing prices, or seeing how much your salary has changed, percentage change puts the difference into meaningful perspective.
The Percentage Change Formula
The percentage change between an old value and a new value is calculated as:Percentage Change = ((New Value − Old Value) / |Old Value|) × 100%A positive result means the value increased, while a negative result means it decreased. The absolute value in the denominator ensures the formula works correctly even when the original value is negative.
Step-by-Step Examples
Example 1: Price Increase
A shirt originally costs $40 and goes up to $50. What is the percentage increase?
- New value − old value = 50 − 40 = 10
- Divide by old value: 10 / 40 = 0.25
- Multiply by 100: 0.25 × 100 = 25%
- The price increased by 25%.
Example 2: Price Decrease
A stock was $120 and falls to $96. What is the percentage decrease?
- 96 − 120 = −24
- −24 / 120 = −0.20
- −0.20 × 100 = −20%
- The stock decreased by 20%.
Percentage Increase vs. Percentage Points
Do not confuse percentage change with percentage point change. If an interest rate goes from 5% to 7%, it increased by 2 percentage points, but the percentage change is (7 − 5) / 5 × 100 = 40%. Both are valid — they just measure different things. Always be clear about which one you mean.
Real-World Uses
- Stock market: daily, monthly, and annual returns
- Sales: tracking month-over-month or year-over-year growth
- Inflation: measuring changes in the cost of living
- Pay raises: calculating the percentage increase of a salary
- Discounts: figuring out what percentage off a sale price represents
- Population: growth rate of cities or countries
- Weight loss / gain: tracking progress as a percentage of starting weight
- Test scores: improvement from one exam to the next
Reverse Calculation: Finding the New Value
If you know the original value and the percentage change, the new value is:New Value = Old Value × (1 + Percentage Change / 100)For example, $500 invested with a 7% return = 500 × 1.07 = $535. For a decrease, use a negative percentage: $500 − 7% = 500 × 0.93 = $465.
Rule of 72
A quick mental trick: to estimate how long it takes something to double at a given growth rate, divide 72 by the percentage. At 6% annual growth, it takes about 72 / 6 = 12 years to double. This is a useful shortcut for investments, savings, and population growth.
Frequently Asked Questions
Why use percentages instead of raw numbers?
Percentages make it easy to compare changes of different magnitudes. A $10 price increase is huge for a $20 item (50%) but trivial for a $2,000 item (0.5%). Percentage change puts everything on a common scale.
What if the original value is zero?
Percentage change is undefined when the original value is zero — you cannot divide by zero. In these cases, it is better to report the absolute change or use a different metric.
How do I calculate percentage difference between two numbers?
For symmetric percentage difference (neither value is the "original"), use: (Value 1 − Value 2) / ((Value 1 + Value 2) / 2) × 100%. This gives the same result regardless of which value you list first.