Percentage Difference Calculator
Our free percentages calculator solves percentage difference problems. Get worked examples, visual aids, and downloadable results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Percentage Difference = (|Value A - Value B| / ((Value A + Value B) / 2)) x 100
Where Value A and Value B are the two numbers being compared. The absolute difference is divided by the average of the two values, then multiplied by 100 to express as a percentage. This formula is symmetric, meaning the result is the same regardless of which value is A or B.
Worked Examples
Example 1: Comparing Two Store Prices
Problem:Store A sells a blender for $89.99 and Store B sells the same model for $109.99. What is the percentage difference?
Solution:Absolute Difference = |89.99 - 109.99| = 20.00\nAverage = (89.99 + 109.99) / 2 = 99.99\nPercentage Difference = (20.00 / 99.99) x 100\n= 0.2000 x 100\n= 20.00%
Result:The prices differ by 20.00% (percentage difference)
Example 2: Comparing Lab Measurements
Problem:Two instruments measure the same sample: Instrument A reads 3.42 g and Instrument B reads 3.57 g. What is the percentage difference?
Solution:Absolute Difference = |3.42 - 3.57| = 0.15\nAverage = (3.42 + 3.57) / 2 = 3.495\nPercentage Difference = (0.15 / 3.495) x 100\n= 0.04292 x 100\n= 4.29%
Result:The measurements differ by 4.29%, indicating reasonable agreement
Frequently Asked Questions
What is percentage difference and how is it calculated?
Percentage difference measures how far apart two values are relative to their average, expressed as a percentage. The formula is: Percentage Difference = (|Value A - Value B| / ((Value A + Value B) / 2)) x 100. Unlike percentage change, percentage difference does not assume a direction or starting point. It treats both values symmetrically. For example, the percentage difference between 40 and 60 is |40-60| / ((40+60)/2) x 100 = 20/50 x 100 = 40%. This is the same regardless of which value you call A or B, making it ideal for comparing two independent measurements where neither is the baseline.
What is the difference between percentage difference and percentage change?
Percentage difference and percentage change answer fundamentally different questions and use different formulas. Percentage change asks how much did a value increase or decrease from a specific starting point, using that starting point as the denominator. Percentage difference asks how far apart are two values relative to their midpoint, using the average as the denominator. For values 80 and 100: percentage change from 80 to 100 is 25%, but from 100 to 80 it is -20%. Percentage difference between them is always 22.2% regardless of order. Use percentage change when there is a clear before-and-after; use percentage difference when comparing two independent measurements.
When should you use percentage difference instead of other metrics?
Use percentage difference when comparing two values that are independent and neither serves as a clear reference or baseline. Common scenarios include comparing prices at two different stores, comparing measurements from two different instruments, comparing performance metrics of two competing products, or comparing test scores from different tests. For example, if Store A sells a product for $45 and Store B sells it for $52, percentage difference gives a symmetric measure of how far apart the prices are. You should not use percentage difference when one value clearly precedes the other in time or when one value is a known standard, as percentage change or percent error would be more appropriate in those cases.
Can percentage difference exceed 100 percent?
Yes, percentage difference can exceed 100% and theoretically can reach up to 200% for positive values. This happens when the two values are very far apart relative to their average. For example, the percentage difference between 10 and 100 is |10-100| / ((10+100)/2) x 100 = 90/55 x 100 = 163.6%. The maximum percentage difference of 200% occurs when one value is zero and the other is positive (or negative). If both values have the same sign, the percentage difference ranges from 0% (identical values) to 200% (one value is zero). When values have opposite signs, the percentage difference can theoretically be even higher, though such cases require careful interpretation.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy