Algebra and Number

Percentage Difference Calculator

Compare two values without designating either one as the original or baseline value.

Percentage difference—

How to calculate percentage difference

  1. Enter Value A and Value B. Their order does not matter because this comparison is symmetric.
  2. The tool finds their absolute difference and divides it by the average of their absolute magnitudes, then multiplies by 100.
  3. Read the percentage and intermediate values. For a directional increase or decrease from a starting value, use percent change instead.

Percentage difference formula, example, and interpretation

This calculator uses percentage difference = |A - B| / ((|A| + |B|)/2) × 100%. The denominator is the average magnitude of the two inputs, so neither is privileged as a baseline. For nonnegative inputs this is the familiar absolute difference divided by their arithmetic mean.

For A = 80 and B = 100, the absolute gap is 20 and average magnitude is 90. Therefore 20/90 × 100 = 22.2222%. Reversing A and B produces the same answer. A result of 0% means equal values; if one input is zero and the other is nonzero, this definition gives 200%.

Percent change asks a different question: (new - old)/|old| × 100% when the old value is nonzero. From 80 to 100, percent change is +25%; from 100 to 80 it is -20%. The 22.2222% difference answers neither directional question, so do not label it an increase or decrease.

Using magnitudes makes the denominator nonnegative even when inputs have opposite signs; for -10 and 10, the difference is 200%. Some fields use alternative signed-average conventions, which may be undefined or yield different results around zero. When both values are zero, the formula is 0/0; this tool displays 0% by the equal-values convention and explicitly notes the exception.

Inputs and results

物品MeaningCheck
Value AFirst number in the pair.May be zero or negative, but must be finite.
Value BSecond number in the pair.Swapping A and B does not change the answer.
Average magnitudeThe mean of |A| and |B|.Avoids a signed zero denominator for opposite values.
Percentage differenceNonnegative, nondirectional comparison.Equal zero values use an explicit 0% convention.

Practical uses and limitations

Measurement comparison

Compare two readings when neither instrument is designated the reference standard.

Quote comparison

Compare two prices symmetrically; use percent change only when one price is the original.

Data review

Spot the relative size of a gap across pairs with different numerical scales.

Limits

A large percentage does not establish statistical significance or measurement error. The chosen denominator convention must match your field or assignment.

常见问题

Is percentage difference the same as percent change?

No. Difference is symmetric and nonnegative; change uses an original value and has a direction.

Why can the result be 200%?

With this average-magnitude denominator, comparing zero to a nonzero number or equal-magnitude opposite signs gives 200%.

What happens when both values are zero?

The raw formula is undefined because it divides 0 by 0. This calculator reports 0% by a stated equal-values convention.

Can I use negative inputs?

Yes. Absolute magnitudes define the denominator, so the result remains nonnegative. Other published conventions may differ.

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Last reviewed: October 26, 2026. Calculations run in your browser. Check rounding and assumptions before using a result in consequential work.

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