Find the percentage difference between two numbers. Unlike percentage change, this compares both numbers to their average, so the answer stays the same no matter which order you enter them.
The absolute difference between the two values is found.
That is divided by the average of the two values, not by either one of them.
Because the base is the average, swapping the two inputs gives an identical answer.
Percentage difference: |A − B| ÷ ((A + B) ÷ 2) × 100
Base: The average of the two values
Comparing two measurements: 40 and 60.
Value A: 40
Value B: 60
Difference: |40 − 60| = 20
Average: (40 + 60) ÷ 2 = 50
Percentage difference: 20 ÷ 50 × 100 = 40%
Answer: 40% difference
A percentage difference calculator tells you how far apart two numbers are, as a percentage of their average. Neither number is treated as the starting point. That makes it the right tool when you compare two things side by side rather than one thing before and after.
Suppose one kirana shop sells a kilogram of toor dal for ₹132 and another sells it for ₹145. Neither price is the 'original', so percentage change would give two different answers depending on which shop you start from. Percentage difference gives one answer that stays the same whichever order you enter them. Students also meet it in physics and chemistry practicals when comparing two measured values, and analysts use it to compare two quotes, two survey results or two readings of the same quantity.
1. Take the two values A and B.
2. Find the absolute difference |A − B|, ignoring the sign.
3. Find the average (A + B) ÷ 2.
4. Divide the difference by the average.
5. Multiply by 100: percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100.
6. If the two values have opposite signs or their average is zero, treat the answer with caution, because the base is not meaningful.
Percentage change divides by the old value, so it is lopsided: 40 to 60 is a 50% rise, but 60 to 40 is a 33.3% fall. When there is no before and after, picking either value as the base is arbitrary. Using the average puts the base in the middle, so swapping A and B leaves the answer unchanged. For 40 and 60 the average is 50 and the difference 20, giving 40%. That number sits between 33.3% and 50%, as a fair middle view should.
For two positive numbers the result can never reach 200%. As one number shrinks towards zero, the difference approaches the other number and the average approaches half of it, so the ratio approaches 2. When one value is exactly zero and the other positive, the answer is exactly 200%. If both values are zero, the average is zero and the result is undefined, which the calculator reports. With values of opposite signs the average can be tiny, producing huge percentages that carry little meaning, so percentage difference is best kept for positive quantities.
In a lab, if you compare your measured value with an accepted or textbook value, the correct measure is percentage error: |measured − accepted| ÷ accepted × 100. There the accepted value is a natural base. Percentage difference is for comparing two measurements of equal standing, such as readings from two students or two instruments. Using the wrong one does not change the difference but changes the denominator, and the resulting number can be noticeably different when the values are far apart.
Farhan finds that one shop in his lane sells a kilogram of toor dal for ₹132 while the supermarket nearby charges ₹145 for the same brand.
Absolute difference: |132 − 145|
Average of the two: (132 + 145) ÷ 2
Difference as a percentage: 13 ÷ 138.5 × 100
Answer: Percentage difference 9.3863%; Average of the two 138.5
Using percentage difference for a price that changed over time; a before-and-after move needs percentage change.
Dividing by the larger or the smaller value instead of the average, which gives an answer that depends on order.
Reporting the result as a percentage 'increase', when percentage difference has no direction.
Applying it to values of opposite sign, where the average can be near zero and the result explodes.
Comparing prices of the same product at two shops or on two shopping apps.
Checking agreement between two readings in a school or college practical.
Comparing two contractor or vendor quotations for the same work.
Comparing results of two surveys, two districts or two batches where neither is a baseline.
How is this different from percentage change?
Percentage change has a direction — it measures a move from an old number to a new one, so 40 to 60 is a 50% increase. Percentage difference has no direction, and uses the average as its base, giving 40%. Use change for before-and-after, and difference for comparing two separate measurements.
Can the percentage difference exceed 100%?
Yes. For two positive numbers the percentage difference can approach 200% but never exceed it; it reaches exactly 200% only when one of the numbers is zero. With negative numbers the result can be larger.