Percentage Change Calculator
Measure the increase or decrease from an original value to a new value, and the symmetric percentage difference between them.
Result
Percentage change: 25%
Change is measured against the magnitude of the original value.
- Signed difference
- 20
- Absolute difference
- 20
- Percentage difference
- 22.22%
- Symmetric: the difference over the mean of the two values
- Direction
- Increase
https://calcgallery.com/everyday-math/percentage-change-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Percentage Change Calculator
- Enter the original value first and the new value second.
- Read the signed percentage and the absolute numerical difference.
- Check the direction label before describing the result as an increase or decrease.
- Use the percentage difference row when neither value is the starting point, such as two quotes or two measurements.
Difference relative to the starting value
First subtract the original value from the new value. Then divide that signed difference by the magnitude of the original:
percentage change = (new − original) ÷ |original| × 100%The original cannot be zero. Percentage change is directional.
Percentage difference, when neither value comes first
Two lab readings, two supplier quotes or two sensor outputs have no starting value, so dividing by either one would favour it. Percentage difference divides by their average instead:
percentage difference = |new − original| ÷ ((original + new) ÷ 2) × 100%It is always positive and does not depend on the order. For two positive values it also sits between the sizes of the two percentage changes: from 80 to 100 is a 25% increase, from 100 to 80 a 20% decrease, and the difference falls between 20% and 25%. The page shows it only while the average is above zero.
The percentage foundation follows OpenStax. Percentage difference follows the definition in Clemson University’s physics lab tutorial: the absolute difference of two measured values divided by their average.
With your numbers
- Difference = 100 − 80 = 20.
- Percentage difference = |difference| ÷ mean of the two values = 22.2222%.
- Percentage change = difference ÷ original magnitude = 25%.
Quick reference
Change is measured against the magnitude of the original value.
| Example | Percentage change |
|---|---|
| 80 to 100 | 25% |
| 100 to 80 | -20% |
| 50 to 50 | 0% |
| 25 to 30 | 20% |
| 200 to 150 | -25% |
| 0.5 to 0.75 | 50% |
Common questions about the Percentage Change Calculator
- Why is the original value in the denominator?
- Percentage change expresses the difference relative to the starting magnitude, so changing 20 from a base of 80 is 25%.
- Can the original value be zero?
- No. Relative change from zero would require division by zero and is undefined.
- Is percentage change symmetric?
- No. Going from 80 to 100 is a 25% increase, while returning from 100 to 80 is a 20% decrease because the bases differ.
- What is the difference between percentage change and percentage difference?
- Percentage change measures from a starting value, so its direction and its base matter. Percentage difference compares two values on equal terms: the gap between them divided by their average, always positive, and the same whichever way round they are entered.
- Why is there sometimes no percentage difference?
- The average of the two values is the reference. When one value is negative and the average is zero or below, dividing by it gives no meaningful percentage, so the row is left out rather than showing a negative or infinite figure.
- What does a negative result mean?
- It means the new value is below the original. The direction row also labels it as a decrease.