Percentage Change — Definition, Formula & Examples
Percentage change is the amount a value has gone up or down, expressed as a percentage of the original value. A positive result means an increase, while a negative result means a decrease.
Percentage change is the ratio of the difference between a new value and an original value to the original value, multiplied by 100. It quantifies the relative magnitude and direction of change from an initial reference point.
Key Formula
Where:
- = The value after the change (the "after" number)
- = The value before the change (the "before" number)
How It Works
To find the percentage change, subtract the original value from the new value, divide by the original value, then multiply by 100. The original value is always your starting point — the "before" number. If the result is positive, the value increased; if negative, it decreased. You can use percentage change to compare shifts in prices, populations, test scores, or any measurable quantity over time.
Worked Example
Problem: A jacket was priced at $80 and is now on sale for $60. What is the percentage change in price?
Step 1: Find the difference between the new value and the original value.
Step 2: Divide the difference by the original value.
Step 3: Multiply by 100 to convert to a percentage.
Answer: The price decreased by 25%.
Another Example
Problem: A town's population grew from 4,000 to 5,200. What is the percentage change?
Step 1: Subtract the original value from the new value.
Step 2: Divide the difference by the original value.
Step 3: Multiply by 100 to express as a percentage.
Answer: The population increased by 30%.
Why It Matters
Percentage change appears constantly in middle-school and high-school math courses whenever you work with data, statistics, or real-world problem solving. Retailers use it to describe discounts, news reports use it to describe economic shifts, and scientists use it to track experimental results. Mastering this concept prepares you for topics like compound interest, growth rates, and data analysis in algebra and beyond.
Common Mistakes
Mistake: Dividing by the new value instead of the original value.
Correction: Always divide by the original (starting) value. The denominator in the formula is the "before" number, not the "after" number.
Mistake: Forgetting to check whether the result should be positive or negative.
Correction: If the new value is smaller than the original, the percentage change is negative, meaning a decrease. Do not drop the negative sign — it tells you the direction of the change.