What is the difference between percentage difference and percentage change?

Percentage change measures how much a value increased or decreased from a specific starting point — it has a clear "old" and "new" value. Percentage difference compares two values when neither is the reference point, using the average of both as the denominator. For example, comparing this year's sales to last year's uses percentage change. Comparing the sales of two different stores uses percentage difference.

Percentage Difference — Definition, Formula & Examples

Percentage difference is a way to compare two values by showing how far apart they are as a percentage of their average. It treats both values equally — neither one is considered the "starting" or "original" value.

The percentage difference between two non-zero values $a$ and $b$ is defined as the absolute difference of the values divided by the mean of those values, multiplied by 100. Because the denominator is the average of both values, percentage difference is symmetric: swapping $a$ and $b$ produces the same result.

Key Formula

\text{Percentage Difference} = \frac{|a - b|}{\dfrac{a + b}{2}} \times 100

Where:

$a$ = First value
$b$ = Second value
$|a - b|$ = Absolute difference (always positive)
$\dfrac{a + b}{2}$ = Average (mean) of the two values

How It Works

Use percentage difference when you have two values and neither one is clearly the "original" or "reference" value. For example, comparing the population of two cities or the prices of two products. You find the absolute difference between the two numbers, divide by their average, and multiply by 100 to convert to a percent. The result tells you how large the gap is relative to the size of the values themselves.

Worked Example

Problem: A basketball team scored 80 points in Game 1 and 60 points in Game 2. What is the percentage difference between the two scores?

Find the absolute difference: Subtract the smaller value from the larger (or use absolute value).

|80 - 60| = 20

Find the average of the two values: Add the two scores and divide by 2.

\frac{80 + 60}{2} = \frac{140}{2} = 70

Divide and multiply by 100: Divide the difference by the average, then convert to a percent.

\frac{20}{70} \times 100 \approx 28.57\%

Answer: The percentage difference between the two scores is approximately 28.57%.

Another Example

Problem: Store A sells a backpack for $45 and Store B sells a similar backpack for $50. What is the percentage difference in price?

Find the absolute difference: Subtract the two prices.

|45 - 50| = 5

Find the average: Add the prices and divide by 2.

\frac{45 + 50}{2} = \frac{95}{2} = 47.50

Calculate the percentage difference: Divide the difference by the average and multiply by 100.

\frac{5}{47.50} \times 100 \approx 10.53\%

Answer: The percentage difference in price is approximately 10.53%.

Visualization

Why It Matters

Percentage difference comes up in science classes whenever you compare experimental results from two trials without a known "correct" value. It is also widely used in business and economics to compare data like salaries, prices, or performance metrics between two groups. Mastering this concept builds a foundation for statistics and data analysis courses in high school and beyond.

Common Mistakes

Mistake: Dividing by just one of the two values instead of their average.

Correction: Percentage difference specifically uses the average of both values as the denominator. Dividing by a single value gives you percentage change, which is a different calculation.

Mistake: Forgetting the absolute value and getting a negative result.

Correction: Percentage difference is always positive (or zero) because it measures the size of the gap, not the direction. Always take the absolute value of the difference.

Related Terms

Decimal — Result is often expressed as a decimal first
Fraction — The formula is built on dividing two quantities
Ratio — Percentage difference is a type of ratio comparison
Numerator — The absolute difference sits in the numerator
Denominator — The average of both values serves as the denominator
Fraction Rules — Simplifying the formula uses fraction operations