How to Calculate Percentage Change
Percentage change measures how much a value has risen or fallen relative to its original amount. The original value is the denominator because it represents the starting point of the comparison.
- Subtract the original value from the new value.
- Divide the difference by the original value.
- Multiply the result by 100.
- A positive result is an increase, while a negative result is a decrease.
Percentage Increase from 100 to 120
Find the numerical increase.
Compare the increase with the starting value.
Convert the decimal result into a percentage.
The value increased by 20, which is a20% increase relative to the original value of 100.
Percentage Decrease from 200 to 150
The calculation is((150 − 200) ÷ 200) × 100, which equals −25%. The negative sign means the value decreased, so this is described as a 25% decrease.
Increase, Decrease, or No Change
The new value is higher than the original value, so the change is a percentage increase.
The new value is lower than the original value, so the change is a percentage decrease.
The two values are equal, so there has been no percentage change.
Percentage Change vs Percentage Difference
Percentage change compares an earlier value with a later value. The calculation has a clear direction, and the original value is used as the reference.
Percentage difference compares two values when neither is naturally the starting value. It normally divides the absolute difference by the average of the two values.
| Measurement | Best used when | Reference value |
|---|---|---|
| Percentage change | Comparing an old value with a new value | Original value |
| Percentage difference | Comparing two values without a time order | Average of both values |
What the Change Multiplier Means
The multiplier compares the new value directly with the original value.
A multiplier of 1.2× means the new value is 1.2 times the original value, which is equivalent to a 20% increase. A multiplier of 0.75× means the new value is 75% of the original, which is equivalent to a 25% decrease.
Common Percentage Change Examples
A 25% price increase.
A 10% salary increase.
A 30% traffic increase.
A 15% revenue decrease.
A 5% population increase.
A 20% decrease.
What Happens When the Original Value Is Zero?
Standard percentage change cannot be calculated when the original value is zero because the formula would require division by zero.
You can still report the absolute increase, such as “the value rose from 0 to 50,” but there is no finite standard percentage increase.
Percentage Change with Negative Values
Percentage change becomes less intuitive when the original value is negative. The standard formula still produces a mathematical result, but the ordinary words “increase” and “decrease” can become misleading.
For example, moving from −100 to −50 is an improvement of 50 units, but dividing by −100 produces −50%. Because of this ambiguity, comparisons involving negative starting values should include the actual values and the absolute change, not only a percentage.
Successive Percentage Changes
Successive percentage changes should not normally be added because each change is applied to a different base.
Increasing 100 by 20% produces 120. Decreasing 120 by 20% removes 24, leaving 96. Therefore, a 20% increase followed by a 20% decrease produces an overall4% decrease, not zero change.
Find the Original or New Value
A value of 200 increased by 15% becomes 230.
If a value is 230 after a 15% increase, the original value was 200.
Common Percentage Change Mistakes
- Dividing by the new value instead of the original value.
- Forgetting to multiply the decimal result by 100.
- Describing a negative result without explaining that it represents a decrease.
- Treating percentage change and percentage difference as the same calculation.
- Claiming a standard percentage increase from an original value of zero.
- Adding successive percentage changes without compounding them.