Four clear steps
How to calculate percentage change
To calculate percent change, keep the values in chronological order and use the old value as the base. When calculating percent change, retain the sign so the result still shows whether the value rose or fell.
- 1Identify the old and new values
The old value is the starting point; the new value is the later amount.
- 2Find the signed change
Subtract old from new. Do not automatically remove a minus sign.
- 3Divide by the old value
This compares the change with the amount you started with.
- 4Multiply by 100 and interpret
Positive means increase; negative means decrease; zero means no change.
Increase example
Percentage change from 100 to 125
Subtract 100 from 125 to get 25. Divide 25 by the old value of 100, then multiply by 100.
((125 - 100) / 100) x 100 = 25%Decrease example
Percentage change from 80 to 64
The signed change is 64 - 80 = -16. Dividing by 80 gives -0.2, so the result is -20%, or a 20% decrease.
((64 - 80) / 80) x 100 = -20%Reference examples
Percent change examples
These examples use exactly the same equation for increases, decreases, and no change.
| Old | New | Change | Working | Answer |
|---|---|---|---|---|
| 100 | 125 | +25 | (25 / 100) x 100 | 25% increase |
| 80 | 64 | -16 | (-16 / 80) x 100 | 20% decrease |
| 50 | 75 | +25 | (25 / 50) x 100 | 50% increase |
| 200 | 150 | -50 | (-50 / 200) x 100 | 25% decrease |
| 90 | 90 | 0 | (0 / 90) x 100 | 0% change |
Choose the right comparison
Percentage change is not percentage difference
The right formula depends on whether one value is a starting point or the two values are peers.
Percentage change
Use for old-to-new movement in either direction.
- Base
- Old value
- Can be negative?
- Yes
Percentage increase
Use when the new value is higher and growth is the focus.
- Base
- Original value
- Direction
- Upward
Percentage difference
Use when neither value is a starting point.
- Base
- Average of both
- Can be negative?
- No
A common confusion
Percent change vs percentage points
When a rate moves from 20% to 25%, it rises by 5 percentage points. Its relative percentage change is 25% because the 5-point rise is one quarter of the old 20% rate.
((25 - 20) / 20) x 100 = 25%Limits and edge cases
When the standard equation needs context
Old value is zero
The formula is undefined because division by zero is impossible. State the absolute change instead.
Negative old values
Standard percent change can be misleading across negative values. Report the raw values and absolute movement with context.
Result above 100%
This is valid. A rise from 50 to 125 is a 150% increase because the increase is 1.5 times the old value.
Decimal answer
Keep full precision while working and round only the final answer, usually to one or two decimal places.
Check your working
Common percent change mistakes
Dividing by the new value
Percentage change compares the movement with where it started, so the old value belongs in the denominator.
Dropping the direction
A negative answer has meaning: it shows a decrease. Keep the sign or clearly label the result as a decrease.
Using percentage difference instead
Percentage difference uses the average of two peer values. Percentage change uses the old value because the comparison has a direction.
Rounding during the calculation
Keep the full decimal until the final step, then round the final percentage to a useful number of decimal places.
Check your result
Calculate percentage change online
Enter the old and new values to see the signed change, direction, formula, and working together.
Open the percentage change calculatorFAQ
Percentage change questions, answered
What is the percentage change formula?
The percentage change formula is ((new value - old value) / old value) x 100.
How do you calculate percent change?
Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is an increase and a negative result is a decrease.
What is the percentage change from 80 to 64?
The change is -16. Divide -16 by 80 and multiply by 100 to get -20%, which means a 20% decrease.
Can percentage change be more than 100%?
Yes. If the increase is larger than the entire old value, the percentage change is greater than 100%. For example, 50 to 125 is a 150% increase.
Can you calculate percentage change from zero?
The standard formula is undefined when the old value is zero because it would require division by zero. Report the absolute change and provide context instead.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an old value and divides by the old value. Percentage difference compares two values without a time order and divides by their average.