When you compare two numbers, the numerical difference alone doesn’t always tell the full story. A gap of 10 might be small in one situation but quite large in another, depending on the values being compared.
Percentage difference provides a useful way to describe that gap relative to the two values. Unlike percentage increase or decrease, it does not treat either number as the starting point.
This guide explains the percentage difference formula, walks through several examples, and shows when this calculation is useful.
What Is Percentage Difference?
Percentage difference describes the relative gap between two values when neither value is considered the original amount.
For example, if two measurements are 80 and 100, you can calculate how far apart they are without saying that one measurement changed into the other.
The calculation uses the absolute difference between the values and compares it with their average.
Percentage Difference Formula
The standard formula is:
Percentage Difference = |Value 1 − Value 2| ÷ ((Value 1 + Value 2) ÷ 2) × 100
The vertical bars indicate that the absolute difference should be used. This means the order of the two values will not make the final result negative.
The average of the two values is used as the reference point.
How to Calculate Percentage Difference Step by Step
Let’s compare two values: 80 and 100.
Step 1: Find the Difference
Subtract the smaller value from the larger value:
100 − 80 = 20
Step 2: Calculate the Average
Add both values and divide the total by two:
(80 + 100) ÷ 2 = 90
Step 3: Divide the Difference by the Average
20 ÷ 90 = 0.2222
Step 4: Convert the Result to a Percentage
0.2222 × 100 ≈ 22.22%
Therefore, the percentage difference between 80 and 100 is approximately 22.22%.
Percentage Difference vs. Percentage Change
Percentage difference and percentage change are used for different types of comparisons.
Percentage change is normally used when there is an original value and a new value. The original value becomes the reference point.
Percentage difference is used when you’re comparing two values without identifying one as the starting value. Their average is used as the reference instead.
For example, if a price changes from $80 to $100, you can calculate the percentage increase using $80 as the original amount. If you’re simply comparing two measurements of 80 and 100, percentage difference may be more suitable.
Percentage Difference vs. Percentage Increase
Percentage increase measures how much a value has grown from its original amount.
Suppose a value changes from 80 to 100.
The percentage increase is:
(100 − 80) ÷ 80 × 100 = 25%
So, the percentage increase is 25%.
The percentage difference between the same values is approximately 22.22% because it uses their average rather than the original value of 80.
Understanding this distinction helps you choose the right formula for the comparison you’re making.
How to Calculate Percentage Difference Between Two Prices
Imagine one store sells a product for $120, while another store lists it for $150.
First, find the difference:
$150 − $120 = $30
Next, calculate the average:
($120 + $150) ÷ 2 = $135
Now divide the difference by the average:
($30 ÷ $135) × 100 ≈ 22.22%
The percentage difference between the two prices is approximately 22.22%.
How to Calculate Percentage Difference Between Two Measurements
This calculation can also be useful when comparing measurements.
Suppose one measurement is 45 cm and another is 50 cm.
First find the difference:
50 − 45 = 5
Then find the average:
(45 + 50) ÷ 2 = 47.5
Finally:
(5 ÷ 47.5) × 100 ≈ 10.53%
The percentage difference is approximately 10.53%.
How to Calculate Percentage Difference Between Test Results
You can use the same method to compare test results.
Suppose two test scores are 72 and 84.
Difference:
84 − 72 = 12
Average:
(72 + 84) ÷ 2 = 78
Percentage difference:
(12 ÷ 78) × 100 ≈ 15.38%
Therefore, the percentage difference between the two results is approximately 15.38%.
Can Percentage Difference Be Greater Than 100%?
Yes. In some cases, percentage difference can be greater than 100%.
Consider the values 1 and 5.
The difference is:
5 − 1 = 4
The average is:
(1 + 5) ÷ 2 = 3
Now calculate:
(4 ÷ 3) × 100 = 133.33%
Therefore, the percentage difference is approximately 133.33%.
This is one reason percentage difference should not be confused with percentage increase or decrease.
What Happens When the Two Values Are the Same?
If two values are exactly the same, there is no difference between them.
For example:
50 and 50
The difference is:
50 − 50 = 0
Therefore, the percentage difference is 0%.
This simply means that the two values are identical.
What Happens When One Value Is Zero?
The standard formula can still be used when one value is zero and the other is not.
For example, compare 0 and 20.
The difference is:
20 − 0 = 20
The average is:
(0 + 20) ÷ 2 = 10
Therefore:
(20 ÷ 10) × 100 = 200%
The percentage difference is 200%.
If both values are zero, however, the standard formula requires division by zero. In that situation, percentage difference is not defined using the usual formula.
How to Use an Online Percentage Calculator
Calculating several pairs of numbers manually can become repetitive. An online calculator can make the process quicker and help you check your work.
You can use the ToolRava Percentage Calculator for common percentage calculations.
A typical process is:
- Open the percentage calculator.
- Enter the numbers required for your calculation.
- Select the appropriate calculation.
- Check the displayed result.
- Review your numbers to make sure they were entered correctly.
An online calculator can be particularly convenient when you’re working with decimal values or several calculations at once.
Common Percentage Difference Examples
Example 1: 40 and 50
Difference:
50 − 40 = 10
Average:
(40 + 50) ÷ 2 = 45
Percentage difference:
(10 ÷ 45) × 100 ≈ 22.22%
Example 2: 200 and 240
Difference:
240 − 200 = 40
Average:
(200 + 240) ÷ 2 = 220
Percentage difference:
(40 ÷ 220) × 100 ≈ 18.18%
Example 3: 500 and 550
Difference:
550 − 500 = 50
Average:
(500 + 550) ÷ 2 = 525
Percentage difference:
(50 ÷ 525) × 100 ≈ 9.52%
Common Mistakes When Calculating Percentage Difference
One common error is using one of the two values as the denominator. That approach is normally associated with percentage increase or decrease when one value is the original reference.
Another mistake is skipping the average calculation. For standard percentage difference, the difference must be compared with the average of the two values.
It’s also important to use the absolute difference. This keeps the result positive even when the order of the values is reversed.
When Should You Use Percentage Difference?
Percentage difference is useful when you’re comparing two values without treating either one as the starting point.
Common situations include:
- Comparing two measurements.
- Comparing prices from different stores.
- Comparing test results.
- Comparing experimental measurements.
- Comparing estimates from different sources.
- Comparing values representing the same type of quantity.
Tips for Getting an Accurate Result
Follow these steps to reduce the chance of making a calculation error:
- Check that you’ve entered both values correctly.
- Find the absolute difference between them.
- Calculate their average.
- Divide the difference by the average.
- Multiply the result by 100.
- Round the final answer only when appropriate.
Frequently Asked Questions
What is the formula for percentage difference?
Divide the absolute difference between two values by their average, then multiply the result by 100.
What is the difference between percentage difference and percentage change?
Percentage change normally uses an original value as its reference, while percentage difference uses the average of the two values.
Can percentage difference be negative?
No. The standard formula uses the absolute difference, so the result is normally expressed as a positive percentage.
Can percentage difference be more than 100%?
Yes. Some pairs of values can produce a percentage difference greater than 100%.
What is the percentage difference between equal numbers?
The result is 0% because identical numbers have no difference between them.
Can I calculate percentage difference with decimals?
Yes. The formula can be used with decimal values as well as whole numbers.
What is the easiest way to calculate percentage difference?
You can use the standard formula manually or use an online Percentage Calculator when you want to complete the calculation more quickly.
Final Thoughts
Percentage difference is a useful way to compare two values when neither one is considered the original or starting amount.
The calculation uses the absolute difference between the values and compares it with their average. This makes it different from percentage increase and percentage decrease, where an original value normally acts as the reference.
Once you know which type of calculation fits your situation, finding percentage difference becomes much easier. For repeated calculations, an online percentage calculator can also save time and help you verify the result.