Two stores quote 80 and 100 for the same item. Neither quote is a starting value, so compare their gap with their average: the percentage difference is 22.22%. Use this method for two non-negative amounts measured in the same unit; use percentage change when you have a before-and-after pair.
What is percentage difference?
Percentage difference measures the difference between two values relative to their average. Unlike percentage increase or percentage decrease, percentage difference treats both numbers equally and does not require one value to be considered the original amount.
This calculation is commonly used in science, statistics, business, quality control, and data analysis.
For example, comparing 80 and 100 results in a percentage difference of 22.22%.
Percentage difference formula
Use this formula to calculate percentage difference:
Percentage Difference = (|Value 1 − Value 2| ÷ ((Value 1 + Value 2) ÷ 2)) × 100
Where:
- Value 1 = the first number
- Value 2 = the second number
- |Value 1 − Value 2| = the absolute difference between the two values
How to calculate percentage difference
Follow these steps:
- Find the absolute difference between the two values.
- Calculate the average of the two values.
- Divide the absolute difference by the average.
- Multiply the result by 100.
Example 1: comparing two prices
Value 1: $80
Value 2: $100
Absolute difference = $20
Average = ($80 + $100) ÷ 2 = $90
Percentage difference = ($20 ÷ $90) × 100 = 22.22%
The percentage difference is 22.22%.
Example 2: comparing test scores
Value 1: 72
Value 2: 84
Absolute difference = 12
Average = (72 + 84) ÷ 2 = 78
Percentage difference = (12 ÷ 78) × 100 = 15.38%
The percentage difference is 15.38%.
Percentage difference table
| Value 1 | Value 2 | Percentage Difference |
|---|---|---|
| 100 | 110 | 9.52% |
| 100 | 120 | 18.18% |
| 80 | 100 | 22.22% |
| 50 | 75 | 40.00% |
| 200 | 250 | 22.22% |
Percentage difference vs. percentage change
These two calculations are often confused.
Percentage change uses the original value as the reference point.
Percentage difference uses the average of both values as the reference point.
For example, comparing 80 and 100:
- Percentage increase from 80 to 100 = 25%
- Percentage decrease from 100 to 80 = 20%
- Percentage difference between 80 and 100 = 22.22%
The results are different because the formulas use different reference values.
When to use percentage difference
Use percentage difference when:
- Comparing two experimental results
- Comparing measurements
- Comparing prices from different stores
- Comparing survey counts measured on the same basis
- Comparing business metrics
- Comparing group measurements on a consistent scale
Common mistakes
Using the original value instead of the average
Many people incorrectly use the percentage increase formula. Percentage difference requires the average of both values.
Ignoring the absolute value
Take the absolute value of the gap so that reversing the two entries does not change the answer. Equal positive values have a difference of 0%, so a valid result is non-negative rather than always positive.
Read the boundaries before using the answer
Enter both values and read the result as it updates. Reset clears both entries and the answer. The absolute difference is the gap in your original unit; the average is the comparison base. Keep that unit consistent: convert centimeters and meters to one unit before comparing them.
For non-negative inputs, this formula gives a result from 0% to 200%. One zero and one positive value give exactly 200%: their gap is twice their average. Two zeros have no percentage result because their average is zero. The calculator reports that boundary instead of displaying 0%.
Negative values are outside this calculator’s model. With signed quantities, such as a loss changing into a profit, the ordinary arithmetic mean can be zero or negative and needs a different interpretation. Compare the absolute amounts separately or state the signed change directly; do not remove a minus sign simply to make the input fit.
Results are rounded only for display, normally to two decimal places. A positive result below 0.005% is shown as less than 0.01%, rather than implying that unequal inputs are identical. Supporting amounts use up to six decimal places, with scientific notation for very small or large values. Ordinary floating-point precision still applies, so keep your original records and avoid entering more significant digits than they support.
If you compare rates such as 20% and 25%, decide which question you need answered. Their percentage-point gap is 5 points; their percentage difference under this formula is 22.22%. A test score comparison also needs a consistent scale: first convert 18/20 and 40/50 to comparable rates rather than comparing the raw correct-answer counts.
Calculation basis
The EPA’s archived definition of relative percent difference uses the absolute gap divided by the average, multiplied by 100. That reference describes duplicate water-quality measurements. It supports the arithmetic here; it does not establish a universal acceptable difference for prices, test scores, laboratory work, or other comparisons.
Frequently asked questions
Is percentage difference always positive?
It is non-negative for the model used here. Equal positive values give 0%. Unequal non-negative values give a positive result. Two zeros have an undefined percentage difference because their average is zero.
Can percentage difference exceed 100%?
Yes. Comparing 10 and 90 gives 160%. For non-negative inputs, the result cannot exceed 200%; it reaches 200% when one value is zero and the other is positive.
When should I use percentage difference instead of percentage change?
Use percentage difference when comparing two values on equal terms, with neither one serving as a starting point. For a before-and-after comparison, use percentage change, which measures the change against the starting value.
What if one value is zero?
Zero and a positive value give 200%. For example, 0 and 50 have a gap of 50 and an average of 25, so 50 divided by 25 times 100 is 200%. Two zeros have no percentage result under this formula.
Can I enter negative values?
This calculator accepts only non-negative values. The arithmetic-mean formula needs additional conventions for signed quantities and may have a zero or negative denominator. Report the signed amounts and the absolute change when this model does not fit.
Does swapping the two values change the result?
No. The absolute gap and the average are unchanged when you reverse the inputs. For example, 80 and 100 give the same 22.22% difference as 100 and 80.
Related Percentage Calculators
Use these calculators for other ways to compare values and percentages:
- Percentage Calculator — solve common percentage problems.
- Reverse Percentage Calculator — work backward from a percentage result to find the original value.
- Fraction Percent Calculator — convert a fraction to a percentage.
- Percent Error Calculator — compare a measured value with an accepted value.
- Percentage Point Calculator — find the percentage-point difference between two percentages.
- Percentage Change Calculator — measure change relative to an original value.