What Is Percentage Change?
Percentage change describes how much a value has increased or decreased relative to a starting value. The starting value acts as the reference point for the calculation.
Percentage Change Formula
The percentage change is calculated by subtracting the original value from the new value, dividing the difference by the original value, and multiplying by 100.
Percentage Change = (New Value − Original Value) ÷ Original Value × 100
What Is Percentage Difference?
Percentage difference is commonly used when comparing two values without designating one of them as the original or starting value. It uses the absolute difference between the values and compares it with their average.
Percentage Difference = |A − B| ÷ [(A + B) ÷ 2] × 100
When to Use Percentage Change
Percentage change is appropriate when there is a clear before-and-after relationship. Examples include comparing a previous price with a new price or comparing a previous measurement with a later measurement.
When to Use Percentage Difference
Percentage difference is useful when comparing two values where neither is necessarily the starting point. It is often useful when evaluating measurements or comparing independently obtained values.
Why the Difference Matters
The same pair of numbers can produce different results depending on which formula is used. Selecting the wrong method can therefore lead to an incorrect interpretation of the size of a change or difference.
Conclusion
Percentage change and percentage difference answer different questions. Percentage change uses an original value as the reference, while percentage difference compares two values without assuming a starting point.
Practical Guide and Examples
Percentage change
Percentage change is used when there is a clear original value and a later value. The formula is (new − original) ÷ original × 100. A positive result indicates an increase and a negative result indicates a decrease.
The original value is the reference point, which is why it appears in the denominator. Changing the denominator changes the question being answered.
Percentage difference
Percentage difference is often used when comparing two values without treating one as the starting point. A common formula divides the absolute difference by the average of the two values, then multiplies by 100.
This makes the calculation symmetric: swapping the two values does not change the result. That is useful when comparing two independent measurements or estimates.
A worked comparison
Suppose a value changes from 100 to 120. The percentage change is (120−100) ÷ 100 × 100 = 20%. If the same two values are treated as independent measurements, percentage difference uses the average, 110, as the reference denominator, giving about 18.18%.
The different answers are not a contradiction. They come from two different definitions and answer different questions.
Why terminology matters
In finance, business, science, and everyday reporting, people sometimes use “percent difference” loosely when they actually mean percentage change. The safest approach is to identify the reference value and state the formula.
If a report or institution provides a specific definition, use that definition rather than assuming the generic formula. Context determines which measure is appropriate.
Common errors
A frequent mistake is using the new value as the denominator when calculating change from an original value. Another is using a signed difference when a symmetric percentage difference calls for an absolute difference.
It is also easy to confuse a percentage change with a percentage-point change when the values themselves are percentages. These distinctions matter when reporting rates, scores, and financial percentages.
Choosing the right calculation
Use percentage change when the story is “from A to B.” Use percentage difference when the question is “how different are A and B?” Then check whether the expected result should be signed or always positive.
A calculator can provide the arithmetic quickly, but the most important step happens before entering the numbers: define what the comparison is intended to mean.
Frequently Asked Questions
When should I use percentage change?
When there is a defined original value and a later value.
When is percentage difference useful?
When comparing two values without treating either as the starting point, using the chosen symmetric definition.
Why can the two methods give different results?
They use different reference denominators and answer different comparison questions.