How to Find Percentage Difference Between Two Numbers: Easy Guide
Updated on April 28, 2026
Percentage difference is a mathematical tool used to compare two values of the same kind to see how much they differ relative to their average. Unlike other percentage calculations, it does not treat one number as the starting point or “correct” value, making it ideal for comparing two independent measurements like the heights of two trees or the costs of items in different stores. Students looking to sharpen their number comparison and percentage skills can explore structured math enrichment resources.
The calculation relies on finding the absolute difference between the two numbers and then dividing that difference by the average of the same two numbers. This result is then converted into a percentage by multiplying by 100. Using the average as the reference point ensures that the result is the same regardless of which number is listed first in the comparison.
In a K-12 math context, percentage difference helps students understand relative size and variation. It is commonly used in science experiments to compare two different experimental results or in statistics to describe the spread between two data points. By mastering this concept, students learn to describe relationships between numbers in a way that remains consistent and objective.
What is percentage difference between two numbers?
Percentage difference is the absolute value of the ratio of the difference between two numbers and their average, expressed as a percentage. It is specifically used when there is no clear “reference” or “original” value to compare against, treating both numbers as equally important in the comparison.
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Percentage Difference Formula
The standard formula for percentage difference is calculated by taking the absolute difference between two values, dividing it by their average, and multiplying the entire fraction by 100 to get the final percentage result. The formula looks like this: Percentage Difference = [ |Value A – Value B| / ((Value A + Value B) / 2) ] × 100.
Absolute Difference vs. Average Value
The numerator of the percentage difference formula is the absolute difference, which represents the physical distance between two numbers on a number line. To find this, you subtract one number from the other and ignore any negative sign, ensuring the result is always positive. This ensures that the comparison focuses on the magnitude of the gap rather than the direction of the change.
The denominator is the average value, which is found by adding the two numbers together and dividing the sum by two. The average serves as the “reference point” or baseline for the comparison. Using the average instead of just one of the numbers provides a balanced perspective, making the percentage difference a non-directional measure of how much the two values vary from one another.
How to Calculate Percentage Difference
To calculate the percentage difference between two numbers, follow these four distinct mathematical steps to ensure accuracy and consistency in your results:
- Calculate the absolute difference by subtracting the smaller number from the larger number.
- Find the average of the two numbers by adding them together and dividing the sum by two.
- Divide the absolute difference from the first step by the average calculated in the second step.
- Multiply the resulting decimal by 100 and add a percentage symbol to the final answer.
By following this specific order, you can compare any two positive quantities. This method is particularly helpful in fields like biology, chemistry, and economics where researchers need to quantify the variation between two separate but related observations without implying that one is the “standard” for the other.
Solved Examples on percentage difference between two numbers
Reviewing solved examples is an effective way to understand how the percentage difference formula applies to real-world scenarios across different subjects. These examples demonstrate how to handle various units of measurement while keeping the core calculation steps identical for every problem.
Example 1: Difference Between Two Prices
A specific video game costs $40 at one retail store and $60 at another online shop. To find the percentage difference between these two prices, first find the absolute difference: $60 – $40 = $20. Next, calculate the average price: ($60 + $40) / 2 = $100 / 2 = $50. Now, divide the difference by the average: $20 / $50 = 0.4. Finally, multiply by 100 to get 40%. The percentage difference between the two prices is 40%.
Example 2: Comparing Heights of Two Objects
Two sunflowers in a garden are measured; one is 150 cm tall and the other is 180 cm tall. The absolute difference between their heights is 180 cm – 150 cm = 30 cm. The average height is (180 cm + 150 cm) / 2 = 330 cm / 2 = 165 cm. Dividing the difference by the average gives 30 / 165, which is approximately 0.1818. Multiplying by 100 results in an 18.18% difference. This tells us the heights of the two sunflowers are roughly 18.2% different from each other relative to their average size.
Example 3: Difference Between Test Scores
On a science quiz, Sarah scored 85 points and Leo scored 95 points. The absolute difference between their scores is 95 – 85 = 10 points. The average of their two scores is (95 + 85) / 2 = 180 / 2 = 90 points. To find the percentage difference, divide 10 by 90 to get approximately 0.1111. When multiplied by 100, the result is 11.11%. Therefore, the percentage difference between Sarah and Leo’s quiz scores is approximately 11.1%.
Example 4: Comparing Monthly Work Hours
One employee worked 120 hours in July, while another employee worked 140 hours in the same month. To compare their workloads using percentage difference, first find the difference: 140 – 120 = 20 hours. Then find the average: (140 + 120) / 2 = 260 / 2 = 130 hours. Divide the difference by the average: 20 / 130 = 0.1538. Multiplying by 100 gives 15.38%. The percentage difference between the hours worked by the two employees is approximately 15.4%.
FAQ
How do you find the percentage difference between two numbers?
To find the percentage difference, you must find the absolute difference between the two values and divide it by their average. First, subtract the smaller value from the larger one. Second, add the two values and divide by two. Third, divide the subtraction result by the average result. Finally, multiply that decimal by 100. This process works for any two positive numbers and provides a single percentage that represents how much they vary from each other without favoring one value as a starting point. It is a standard procedure in many middle and high school math curricula.
Is percentage difference the same as percentage change?
No, percentage difference and percentage change are different. Percentage change is used when there is an “old” value and a “new” value, showing how much something increased or decreased over time. In percentage change, you always divide by the original starting number. Percentage difference is used when both numbers are equally important and there is no “before” and “after” relationship. Because there is no starting number, we divide by the average of the two values instead. Using the wrong formula can lead to very different results, so always check if your data has a clear starting point before choosing.
Can percentage difference be negative?
In standard statistical and mathematical practice, percentage difference is never expressed as a negative number. This is because the formula uses the absolute value of the difference in the numerator. Absolute value measures distance, and distance is always zero or positive. The goal of percentage difference is to show the magnitude of the gap between two values, not the direction. Even if you subtract a larger number from a smaller one, you ignore the minus sign. This makes the calculation non-directional, meaning you will get the same result whether you compare Value A to Value B or Value B to Value A.
Why do we divide by the average instead of the original number?
We divide by the average because in many comparisons, neither number has a logical claim to be the “original” or “reference” value. If you had two different people’s heights, choosing one person as the “base” would result in a different percentage than choosing the other person. For example, if you compare 10 and 20, using 10 as the base gives a 100% difference, but using 20 as the base gives a 50% difference. By using the average (15) as the denominator, you get a consistent result of 66.7% regardless of which number you start with. This provides a fair and neutral comparison.
What is the symbol used for percentage difference?
The most common symbol used for percentage difference is the standard percent sign (%). In more advanced scientific or technical papers, you might see it referred to as “PD” or “RPD” (Relative Percentage Difference). When writing out the results of a calculation, it is standard practice to include the % symbol immediately after the numerical value, such as “15.5%.” In some mathematical contexts, the Greek letter delta (Δ) might be used to represent the difference part of the formula, but for general K-12 schoolwork, the word “percentage difference” followed by the final percent value is the most appropriate way to display the answer.
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