What is percentage change?
Percentage change measures how much a value has increased or decreased relative to its original value. A positive result indicates an increase, while a negative result indicates a decrease.
Percentage increase formula
Subtract the original value from the higher new value, divide by the original value, and multiply by 100. For example, moving from 100 to 120 is a 20% increase.
Percentage decrease formula
The same percentage-change formula applies to a decrease. Moving from 80 to 60 gives −25%, meaning a 25% decrease.
How to calculate percentage change
- Find the difference: new value − original value.
- Divide that difference by the original value.
- Multiply the result by 100 to express it as a percentage.
If the original value is zero and the new value is non-zero, percentage change is undefined because the formula would require division by zero.
Worked examples
| Original | New | Result |
|---|---|---|
| 100 | 120 | 20% increase |
| 80 | 60 | 25% decrease |
| 50 | 50 | 0% change |
| 15 | 10 | 33.33% decrease |
Percentage change vs percentage difference
Percentage change has a direction: one number is the original reference and the other is the new value. Percentage difference treats both values equally and commonly divides their absolute difference by their average. The two calculations answer different questions.
Frequently asked questions
How do I calculate percentage change?
Subtract the original value from the new value, divide the result by the original value, then multiply by 100.
What is the formula for percentage increase?
Percentage increase = ((new value − original value) ÷ original value) × 100 when the result is positive.
What is the formula for percentage decrease?
Use ((new value − original value) ÷ original value) × 100. A negative result indicates a decrease; its magnitude is the percentage decrease.
Can percentage change be negative?
Yes. A negative percentage change normally indicates a decrease, while a positive result indicates an increase. With a negative original value, interpret the formula result in context.
What happens if the original value is zero?
If both values are zero, the change is 0%. If only the original value is zero, percentage change is undefined because division by zero is not possible.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an original reference value. Percentage difference compares two values symmetrically, usually using their average as the denominator.