Percentage Difference Calculator
Quick Answer
Percentage Difference = |A - B| / ((A + B) / 2) × 100. It is symmetric: the order does not matter.
Understanding Percentage Difference
Percentage difference is a way to compare two values when neither is considered the "reference" or "original" value. Unlike percentage change (which is directional -- from old to new), percentage difference is symmetric: comparing A to B gives the same result as comparing B to A.
The Formula
Percentage Difference = |A - B| / ((A + B) / 2) × 100
The numerator is the absolute difference between the two values. The denominator is the average (mean) of the two values. This gives a percentage relative to the midpoint.
When to Use Percentage Difference
- Comparing products: Price of Brand A vs Brand B
- Scientific measurements: Two independent measurements of the same quantity
- Regional comparisons: Average salary in City A vs City B
- Experimental results: Results from two different methods or labs
Percentage Difference vs. Percentage Change
This is the most common source of confusion. Percentage change = ((New - Old) / |Old|) × 100. It has direction (increase or decrease) and uses the old value as base. Percentage difference = |A - B| / ((A+B)/2) × 100. It has no direction and uses the average as base.
Example: Values 50 and 75. Percentage change from 50 to 75 = 50%. Percentage change from 75 to 50 = -33.3%. Percentage difference = |50-75| / 62.5 × 100 = 40%. Note how the difference is the same regardless of order.
Range of Percentage Difference
Percentage difference ranges from 0% (values are identical) to 200% (one value is zero). It cannot exceed 200% when both values are positive. This makes it useful as a bounded measure of dissimilarity.
Frequently Asked Questions
What is percentage difference?
A symmetric measure of how two values differ, using their average as the base. Formula: |A-B| / ((A+B)/2) × 100.
How is it different from percentage change?
Change is directional (old to new); difference is symmetric (order does not matter). Change uses old value; difference uses average.
When should I use percentage difference?
When comparing two independent values with no inherent "before/after" relationship -- like comparing two brands, cities, or methods.
Can percentage difference be more than 100%?
Yes, up to 200%. This occurs when one value is zero. For two positive values, it ranges from 0% to 200%.