How this instrument works
Percentage difference measures how far apart two independent values sit, and it resolves the question every percentage-change calculation avoids: which value counts as the fixed starting point? Here neither does. The formula divides the gap |A − B| by the average of the two, (A + B) ⁄ 2, so Value A and Value B play identical roles — swap the two entries and the result does not move. That symmetry is the entire point: it is built for comparing two independent measurements, like two instruments' readings of the same sample, where calling one of them the 'original' would be arbitrary.
The symmetry is not a coincidence of the numbers chosen — it is guaranteed by the algebra. Reversing the subtraction inside the bars, from A − B to B − A, only flips a sign, and absolute value erases that sign either way, so |A − B| equals |B − A|. The denominator, (A + B) ⁄ 2, does not even notice a swap, since addition never cares about order. Two order-independent pieces, divided, can only produce an order-independent answer — which is exactly why this differs from percentage CHANGE, whose denominator is whichever single value gets called 'old,' making the answer depend entirely on which direction is measured.
There is a genuinely surprising limit built into the formula: for two values sharing the same sign, percentage difference can never exceed 200%, no matter how far apart they are. Push one value toward zero while holding the other fixed and the ratio climbs steadily toward that ceiling but never past it — a fact that trips up anyone expecting percentages to grow without bound the way percentage change does near a small starting value. The one input this sheet refuses is A and B summing to exactly zero, such as 5 and −5, because the average then collapses to zero and the division becomes undefined.
- Enter your first measurement into Value A — either reading can go first, since order never changes the result.
- Enter the second measurement into Value B.
- Read Percentage difference for the symmetric gap between them, expressed as a share of their average.
- To check the symmetry yourself, swap the two entries — Percentage difference stays exactly the same.
Worked example — comparing 50 and 70
Set Value A to 50 and Value B to 70. The gap between them is |50 − 70| = 20, and their average is (50 + 70) ⁄ 2 = 60. Percentage difference is 20 ⁄ 60 × 100, which is exactly 100 ⁄ 3, or 33.33333333333333…%, a repeating decimal the sheet displays rounded to 33.33%.
Swap the entries — Value A now 70, Value B now 50 — and nothing about the answer moves: |70 − 50| is still 20 and (70 + 50) ⁄ 2 is still 60, so Percentage difference reports the same 33.33%. Compare that to percentage change on the same pair: 50 to 70 is a 40% increase, but 70 to 50 is a 28.57% decrease — two different numbers for the same two readings, because percentage change always anchors on whichever value gets called the start.
Questions
How is percentage difference different from percentage change?
Percentage difference divides the gap between two values by their average, (A + B) ⁄ 2, so the answer is identical no matter which one is entered first. Percentage change instead divides by whichever value gets designated the starting point, so the same pair gives different answers depending on direction — 50 to 70 is a 40% increase, but 70 to 50 is a 28.57% decrease. Reach for percentage difference when neither reading is truly 'before' the other.
Why does the formula divide by the average instead of by one of the values?
Because averaging is the one operation that treats Value A and Value B identically — (A + B) ⁄ 2 doesn't change when the two entries are swapped, and neither does |A − B|, so their ratio can't change either. Dividing by a single value instead would force a choice about which reading is the reference point, which is exactly the asymmetry percentage difference is built to avoid when comparing two independent measurements.
Can percentage difference ever exceed 100%?
Yes, up to a hard ceiling of 200%, reached only when one of the two values is zero. For two values sharing the same sign, |A − B| can never exceed A + B, and dividing by half that sum caps the ratio at 2 — so 200% is the largest percentage difference two same-sign numbers can produce, however far apart they are otherwise.
Why is a pair like 5 and −5 rejected?
Because their average is zero — (5 + (−5)) ⁄ 2 = 0 — and the formula divides by that average, which is undefined arithmetic no amount of rounding can fix. This sheet blocks any A and B that sum to exactly zero rather than showing an infinite or nonsensical result.
How does percentage difference differ from a percentage point difference?
A percentage point difference is plain subtraction between two numbers that are already percentages, such as 45% − 40% = 5 percentage points, with no averaging or division involved at all. Percentage difference instead works on any two raw values, not just percentages, and produces its own ratio-based percentage by dividing their gap by their average — the two measures describe entirely different kinds of comparison.
When would percentage difference be preferred over percentage error?
When comparing two independent experimental readings with no accepted 'true' value to check against — two instruments' readings of the same sample, say. Percentage error instead measures a single reading against a known reference or theoretical value, dividing by that reference rather than an average. The symmetry of percentage difference is precisely what makes it unsuited as an error metric: it cannot say which reading, if either, is closer to correct.