Calculate the percentage difference between two numbers relative to their average, plus the absolute gap and the percent change from each value.

Enter both values in the same units. The order does not change the percentage difference.

Display precision

Percentage Difference Formula and How to Use It

This calculator measures how far apart two values are relative to the average of their absolute magnitudes. For nonnegative values, this is the usual average-based percentage difference. Its signed-input extension preserves symmetry: reversing the inputs leaves the result unchanged, and opposite signs give 200%.

Percentage Difference Formula

Percentage Difference = (|A - B|) / ((|A| + |B|) / (2)) × 100
  • A = first value
  • B = second value
  • The numerator measures the absolute gap between the values.
  • The denominator scales that gap by the average of the absolute magnitudes.

How to Calculate Percentage Difference

  1. Find the absolute difference between the two values.
  2. Find the average of the absolute magnitudes of the two values.
  3. Divide the difference by the average.
  4. Multiply by 100 to convert the result into a percentage.
Difference = |A - B|
Average magnitude = (|A| + |B|) / (2)
Percentage Difference = (Difference) / (Average magnitude) × 100

Example

If the two values are 80 and 100, first find the difference, then divide by their average.

(|80 - 100|) / ((80 + 100) / (2)) × 100 = (20) / (90) × 100 ≈ 22.22%

The two values differ by approximately 22.22% relative to their average magnitude.

What the Result Means

  • 0% means the values are equal and nonzero; two zero values are undefined.
  • A small percentage means the values are close together.
  • A large percentage means the gap is large compared with the average absolute magnitude.
  • More than 100% is possible when the difference is larger than the average.

Percentage Difference vs. Percentage Change

These two ideas answer different questions. The directional-change figures here intentionally divide by the signed original value; from a negative baseline, a positive percentage need not mean a numerical rise. This differs from the absolute-baseline convention used by some other calculators.

Measure Best Use Formula
Percentage Difference Compare two values without treating either one as the baseline
(|A - B|) / ((|A| + |B|) / (2)) × 100
Percentage Change Measure increase or decrease from an original value to a new value
(New - Original) / (Original) × 100
Percent Error Compare a measured value to an accepted or true value
(|Measured - Accepted|) / (|Accepted|) × 100

When to Use This Calculator

  • Comparing two lab measurements
  • Checking the spread between two prices
  • Comparing production output from two batches
  • Reviewing differences between survey results
  • Measuring how close two dimensions or estimates are

Important Notes

  • Use the same units for both inputs before calculating.
  • The calculation is symmetric, so switching the inputs does not change the answer.
  • The denominator is zero only when both values are zero, so that case is undefined.
  • Use percentage change instead when one number is clearly the starting value and the other is the ending value.
(|A| + |B|) / (2) = 0 only when A = B = 0

Quick FAQ

Can percentage difference be negative?
No. The formula uses an absolute difference, so the result is always zero or positive.

Can percentage difference be greater than 100%?
Yes. If the gap exceeds the average absolute magnitude, the result exceeds 100%. Under this calculator’s convention the range is 0% to 200%; opposite signs or exactly one zero give 200%.

Why does the formula use the average?
The average absolute magnitude treats neither value as the reference and keeps the denominator nonnegative. For two nonnegative values it equals their ordinary average.

Is percentage difference the same as percent increase?
No. Percent increase and percent decrease require a starting value, while percentage difference compares two values equally.