How to Calculate Percentage Change: Formulas, Examples, and Common Mistakes
Percentage change is one of the most practical mathematical concepts you will encounter. From tracking stock prices and analysing sales data to understanding inflation rates and exam score improvements, percentage change gives you a standardised way to compare how values shift over time. Unlike absolute differences, percentage change accounts for the scale of the original value, making comparisons meaningful.
This guide covers the percentage change formula, the distinction between percentage increase and decrease, percentage difference, successive percentage changes, and common pitfalls. We include multiple worked examples so you can apply these ideas with confidence.
The Percentage Change Formula
The percentage change from an old value to a new value is:
A positive result indicates an increase; a negative result indicates a decrease. The denominator is always the original (old) value, since we are measuring how much the quantity changed relative to where it started.
Percentage Increase
When the new value is greater than the old value, we have a percentage increase:
Example 1: Salary Increase
A salary rises from $50,000 to $54,000. What is the percentage increase?
The salary increased by 8%.
Example 2: Population Growth
A town's population grows from 12,500 to 14,200. Find the percentage increase.
Percentage Decrease
When the new value is less than the old value, we have a percentage decrease. The formula is the same; the result is negative, but we typically state the magnitude:
Example 3: Price Reduction
A laptop originally priced at $1,200 is reduced to $960. What is the percentage decrease?
The price decreased by 20%.
Example 4: Stock Price Drop
A share price falls from $85 to $72.25. Find the percentage decrease.
Percentage Difference
Percentage difference is used when there is no clear “old” and “new” value, and you simply want to compare two quantities. The formula uses the average of the two values as the denominator:
Example 5: Comparing Test Scores
Two students score 78 and 85 on the same exam. What is the percentage difference?
Successive Percentage Changes
When percentage changes happen one after another, they do not simply add up. This is a common source of confusion.
Example 6: Increase Then Decrease
A price of $100 increases by 20%, then decreases by 20%. Is the final price $100?
The final price is $96, not $100. A 20% increase followed by a 20% decrease results in a net 4% decrease. This happens because the decrease is applied to the larger value.
The General Formula
For two successive percentage changes of and , the overall percentage change is:
Using our example: .
Reverse Percentage Problems
Sometimes you know the final value after a percentage change and need to find the original value.
Example 7: Finding the Original Price
After a 15% discount, a jacket costs $68. What was the original price?
The discounted price is 85% of the original (100% - 15% = 85%):
Example 8: Pre-Tax Price
A bill including 8% tax is $162. What was the pre-tax amount?
Percentage Points vs Percentage Change
This distinction trips up many people. If interest rates rise from 3% to 5%, that is a 2 percentage point increase but a percentage increase. These are very different statements. News reports often conflate the two, so always check which is being used.
Common Mistakes
- Wrong denominator: Always divide by the original value for percentage change, not the new value.
- Adding successive percentages: A 10% increase followed by a 10% increase is not a 20% increase. It is 21% (using the compound formula).
- Confusing percentage change with percentage difference: Percentage change requires a clear direction (old to new); percentage difference is symmetric.
- Ignoring scale: A $10 increase on a $100 item (10%) is very different from a $10 increase on a $10,000 item (0.1%).
Try It Yourself
Calculate percentage change instantly with our free Percentage Change Calculator. Simply enter the old and new values to get the percentage change, increase, or decrease. For more general percentage calculations, try our Percentage Calculator which handles “what is X% of Y”, “X is what percent of Y”, and other common percentage problems.
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