Percentage Difference Calculator

Q: What is percentage difference?

The absolute gap between two values divided by their average, expressed as a percentage: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50, that's 10 ÷ 45 = 22.22%.

Q: How is it different from percentage change?

Percentage change divides by the starting value and has a direction — 40 → 50 is +25%, and 50 → 40 is −20%. Percentage difference divides by the average and has no direction: both orders give 22.22%.

First value

Second value

Percentage difference

22.22%

Worked as: |40 − 50| ÷ (( 40 + 50) ÷ 2) × 100 = 22.22%
Absolute gap: 10
Average of the two values: 45
Or measured from the first value: +25%
Or measured from the second value: -20%

Why the same pair can read 20%, 25%, or 33%

Compared against 40	Gap	Average-based	From 40
+5% higher	42	4.88%	+5%
+10% higher	44	9.52%	+10%
+25% higher	50	22.22%	+25%
+50% higher	60	40%	+50%

Use symmetric difference when neither reading is the reference — comparing two scales, two test scores, or two price checks. When one value is the starting point, use the percentage increase calculator or the percentage decrease calculator, which divide by the starting value.

40 and 50 differ by 22.22%. That's the symmetric percentage difference: |40 − 50| ÷ 45 × 100, where 45 is the average of the two numbers — not one of them. Because the denominator is the average, order doesn't matter (50 vs 40 gives the same 22.22%), and the same pair also reads as +25% measured from 40 and −20% measured from 50. All three are correct; they answer different questions.

Why one pair of numbers has three percentages

The percentage you get depends entirely on what you divide by:

symmetric % difference = |a − b| ÷ ((a + b) ÷ 2) × 100
change from a          = (b − a) ÷ a × 100
change from b          = (a − b) ÷ b × 100

On the default pair, 40 and 50:

Absolute gap: 10
Average (the symmetric denominator): 45
Symmetric difference: 10 ÷ 45 × 100 = 22.22%
From 40: +10 ÷ 40 = +25%
From 50: −10 ÷ 50 = −20%

The symmetric figure always lands between the two directional ones, and it's the version to use when there's no "before" — two instruments measuring the same thing, two estimates of the same quantity, two labs reporting the same sample.

Same gap, three readings

Pair	Symmetric difference	vs first value	vs second value
40 / 50	22.22%	+25%	−20%
90 / 100	10.53%	+11.11%	−10%
100 / 120	18.18%	+20%	−16.67%
40 / 60	40%	+50%	−33.33%

The wider the gap, the further apart the three numbers drift: at a 10% gap they're nearly interchangeable, and at a 50% gap they differ by 17 percentage points. That's why "the two numbers disagree by X%" is meaningless until you say which X you mean.

When to use which one

Percentage difference (this page) — two readings of the same quantity, neither one privileged: comparing two scales, two quotes, two measurements of the same part. No direction, order-independent.
Percentage change — there's a clear before and after: a price rose, a count fell. Divides by the starting value. Use the percentage increase calculator or the percentage decrease calculator.
Percentage of — part versus whole: "X is what percent of Y". That's the percentage calculator.

One boundary is worth knowing: when the two numbers add to zero (40 and −40), the average is 0 and the symmetric difference is undefined — the calculator says so instead of printing infinity. And when one value is 0, the symmetric formula still works: 0 vs 10 averages to 5, giving 200%, which is the honest answer for a comparison against nothing rather than a division-by-zero error.

How to use this calculator

Enter the two values (40 and 50 are pre-filled).
Read the symmetric percentage difference — the order-independent figure.
Read the two directional figures underneath to see what the same gap looks like measured from each end.
Open the chart to see how the three numbers diverge as the gap widens.
Swap the two inputs if you like; the symmetric result won't change.

Frequently asked questions

What is percentage difference?

The absolute gap between two values divided by their average, expressed as a percentage: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50, that's 10 ÷ 45 = 22.22%.

How is it different from percentage change?

Percentage change divides by the starting value and has a direction — 40 → 50 is +25%, and 50 → 40 is −20%. Percentage difference divides by the average and has no direction: both orders give 22.22%.

Why doesn't the order of the two numbers matter?

Because the denominator is their average, which is the same either way. |40 − 50| ÷ 45 and |50 − 40| ÷ 45 are identical. That's the point of the symmetric formula — neither reading is treated as the baseline.

When should I use percentage difference?

When you're comparing two measurements of the same thing and neither is the "original": two thermometers, two lab results, two contractor bids. When there is a before and after, use percentage increase or decrease instead.

Why does 0 versus 10 give 200%?

The average of 0 and 10 is 5, and the gap is 10 — so 10 ÷ 5 × 100 = 200%. It looks extreme because a comparison against zero is extreme; the alternative (dividing by zero) has no answer at all.

Why isn't there a result when my two numbers add to zero?

Because the average is then 0, and the formula would divide by it. Pairs like 40 and −40 have no defined percentage difference, so the calculator reports that rather than printing infinity.

Data sources: The symmetric percentage difference is a standard definition — absolute difference divided by the mean of the two values — not an externally published rate, so every figure on this page can be reproduced by entering the same two numbers (40 and 50 are pre-filled). The comparison against percentage change and percentage-of is definitional as well; those have their own pages, linked above. Related tools: percentage increase calculator, percentage decrease calculator, percentage calculator, all math calculators.