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Percent Difference Formula: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Percent Difference FormulaPercent Difference Formula: Definition and ExamplesTable of ContentsPercent Difference Formula: How to Calculate and Use It Definition of Percent Difference

The percent difference formula calculates the relative change between two values when neither is considered a reference point. It involves taking the absolute difference between two values, dividing by their average, and multiplying by 100100100. This formula is particularly useful when comparing values of equal importance or when the magnitude of change matters more than its direction. The mathematical representation of percent difference is: Percent difference=Absolute differenceAverage×100\text{Percent difference} = \frac{\text{Absolute difference}}{\text{Average}} \times 100Percent difference=AverageAbsolute difference​×100

When using the percent difference formula, we always consider the absolute value of the difference, ignoring any negative signs. This helps us focus on the magnitude rather than the direction of change. The formula is most appropriate when comparing values of similar categories (like weights of two children), when magnitude matters more than direction, or when there's no clear reference value. It's important to note that percent difference is always positive and represents the relative variation between values regardless of which value is larger.

Examples of Percent Difference Example 1: Calculating Percent Difference Between Two Prices Problem:

The price of item aaa is $30\$30$30. The price of item bbb is $50\$50$50. Calculate the percent difference between two prices.

Step-by-step solution:

Step 1, Find the two values we're comparing.

In this example, the values we are comparing are 303030 and 505050. a=30,b=50a = 30, b = 50a=30,b=50

Step 2, Find the absolute difference.

Calculate the difference between the two values: Difference=a−b=30−50=−20\text{Difference} = a - b = 30 - 50 = -20Difference=a−b=30−50=−20 Then take the absolute value (remove negative sign if present): Absolute Difference=∣−20∣=20\text{Absolute Difference} = |-20| = 20Absolute Difference=∣−20∣=20 (Note: The order of numbers doesn't matter as we calculate the absolute difference between the two numbers.)

Step 3, Calculate the average of both the values.

Average=a+b2=30+502=802=40\text{Average} = \frac{a + b}{2} = \frac{30 + 50}{2} = \frac{80}{2} = 40Average=2a+b​=230+50​=280​=40

Step 4, Use the percent difference formula to calculate the percent difference.

Percentage difference=2040×100=0.5×100=50%\text{Percentage difference} = \frac{20}{40} \times 100 = 0.5 \times 100 = 50\%Percentage difference=4020​×100=0.5×100=50%

Thus, the percent difference between 303030 and 505050 is 50%50\%50%.

Example 2: Comparing the Prices of Clothing Items Problem:

The price of a sweater is $80\$80$80, and the price of a jacket is $96\$96$96. Calculate the percentage difference.

Step-by-step solution:

Step 1, Identify the two values.

a=$80 and b=$96a = \$80 \text{ and } b = \$96a=$80 and b=$96

Step 2, Calculate the absolute difference between the two values.

Difference=∣$80−$96∣=∣−$16∣=$16\text{Difference} = |\$80 - \$96| = |-\$16| = \$16Difference=∣$80−$96∣=∣−$16∣=$16

Step 3, Find the average of the two values.

Average=a+b2=80+962=1762=88\text{Average} = \frac{a + b}{2} = \frac{80 + 96}{2} = \frac{176}{2} = 88Average=2a+b​=280+96​=2176​=88

Step 4, Apply the percent difference formula.

Percentage difference=1688×100=0.1818×100=18.18%\text{Percentage difference} = \frac{16}{88} \times 100 = 0.1818 \times 100 = 18.18\%Percentage difference=8816​×100=0.1818×100=18.18% Example 3: Comparing Town Populations Problem:

The population of town aaa is 20,00020,00020,000. The population of town bbb is 16,00016,00016,000. What is the percent difference between the population values?

Step-by-step solution:

Step 1, Write down the two values we're comparing.

a=20,000 and b=16,000a = 20,000 \text{ and } b = 16,000a=20,000 and b=16,000

Step 2, Find the absolute difference between the two values.

Absolute difference=∣20,000−16,000∣=∣4,000∣=4,000\text{Absolute difference} = |20,000 - 16,000| = |4,000| = 4,000Absolute difference=∣20,000−16,000∣=∣4,000∣=4,000

Step 3, Calculate the average of the two populations.

Average=a+b2=20,000+16,0002=36,0002=18,000\text{Average} = \frac{a + b}{2} = \frac{20,000 + 16,000}{2} = \frac{36,000}{2} = 18,000Average=2a+b​=220,000+16,000​=236,000​=18,000

Step 4, Use the percent difference formula to find the answer.

Percentage difference=4,00018,000×100=0.2222×100=22.22%\text{Percentage difference} = \frac{4,000}{18,000} \times 100 = 0.2222 \times 100 = 22.22\%Percentage difference=18,0004,000​×100=0.2222×100=22.22% Comments(1)FFoodieEllieNovember 4, 2025I've used this percent difference formula explanation with my students. It's clear and the examples really helped them grasp the concept!

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