Percent Difference Formula - Definition, Steps, Examples

Q: What is the percent difference formula?

$\frac{\lvert a - b \rvert}{(a+b)/2} \times 100$. Divide the absolute gap between the two values by their mean, then multiply by 100.

Key Points

The percent difference formula is $\frac{\lvert a - b \rvert}{(a+b)/2} \times 100$ , dividing the absolute gap by the mean of the two values.
The mean is the denominator because neither value is the original, so neither has a claim to be the base.
The formula is symmetric, so swapping $a$ and $b$ gives the same answer, which percent change never does.
Use percent difference to compare two measurements of equal standing, and percent change when one value genuinely came first.
Because the mean sits between the two values, a percent difference can exceed 100 per cent when the values differ by more than their average.

What Is the Percent Difference Formula?

The percent difference formula compares two values neither of which is a starting point:

$\text{percent difference} = \frac{\lvert a - b \rvert}{\dfrac{a+b}{2}} \times 100$

The numerator is the size of the gap and the denominator is the average of the two values. Both the absolute value and the mean are what make the result independent of which value is named first.

Why the Denominator Is the Mean

Percent change has an obvious base: the value that came first. Percent difference has no such thing, because the two values are peers.

Picking one of them arbitrarily would make the answer depend on the choice. Comparing 40 and 50 gives 25 per cent against the 40 and 20 per cent against the 50, so the same pair would yield two different answers depending on which was written first.

Using the mean removes the arbitrariness. The average of 40 and 50 is 45, and $\frac{10}{45} \times 100 \approx 22.2$ per cent, a single figure that belongs to the pair rather than to either member of it.

Variable Key

Symbol	Meaning	Unit or type	Notes
$a$ , $b$	the two values	same unit	order does not matter
$\lvert a - b \rvert$	absolute gap	same unit	the numerator, never negative
$\frac{a+b}{2}$	mean of the pair	same unit	the denominator
result	percent difference	per cent	symmetric in $a$ and $b$

Examples of the Percent Difference Formula

Example 1

Find the percent difference between 40 and 50.

$\frac{\lvert 40 - 50 \rvert}{\frac{40+50}{2}} \times 100 = \frac{10}{45} \times 100 \approx 22.2$

Final answer: about 22.2 per cent

Example 2

Two laboratories measure a sample as 8.4 and 9.0 units. Find the percent difference by using the first value as the base.

The first reading is written first, so it looks like the reference:

$\frac{0.6}{8.4} \times 100 \approx 7.14$

That is a percent change, not a percent difference, and it carries a hidden claim: that lab one's figure is the correct starting point. Neither lab outranks the other, and swapping the order would give $\frac{0.6}{9.0} \times 100 \approx 6.67$ per cent, a different answer for the same disagreement.

Dividing by the mean of 8.7 removes the asymmetry:

$\frac{0.6}{8.7} \times 100 \approx 6.90$

Final answer: about 6.90 per cent, the same whichever lab is listed first.

Example 3

Find the percent difference between 120 and 80.

$\frac{40}{100} \times 100 = 40$

Final answer: exactly 40 per cent

The mean of 120 and 80 is 100, which makes this one arithmetically clean.

Example 4

Two regions report average incomes of 32,000 and 48,000. Find the percent difference.

$\frac{16000}{40000} \times 100 = 40$

Final answer: 40 per cent

Note that the percent change from 32,000 to 48,000 is 50 per cent, while the change from 48,000 to 32,000 is 33.3 per cent. The percent difference of 40 per cent sits between them, as it always does.

Example 5

Find the percent difference between 1 and 5, and comment on the size of the answer.

$\frac{4}{3} \times 100 \approx 133.3$

Final answer: about 133.3 per cent

A percent difference above 100 per cent is legitimate here, because the gap of 4 exceeds the mean of 3. This cannot happen with percent decrease, which is capped at 100 per cent.

Don't Confuse These Three Comparisons

Measure	Formula	When to use it
Percent difference	$\frac{\lvert a - b \rvert}{(a+b)/2} \times 100$	two values of equal standing
Percent change	$\frac{\text{new} - \text{old}}{\text{old}} \times 100$	one value came first
Percent error	$\frac{\lvert \text{measured} - \text{true} \rvert}{\lvert \text{true} \rvert} \times 100$	one value is a known reference

The choice is about the status of the two numbers, not about the arithmetic. If one value is a true or accepted figure, use percent error; if one came earlier, use percent change; if they are peers, use percent difference.

Percent Difference, Common Confusions Cleared Up

Mistake 1: Using one of the values as the base

Where it slips in: The first value written looks like a reference, and percent change is the more familiar formula.

Don't do this: $\frac{\lvert a - b \rvert}{a} \times 100$

The correct way: Divide by $\frac{a+b}{2}$ . Any formula that gives a different answer when the two values are swapped is computing a change, not a difference.

Students who ask whether either number came first stop reaching for the wrong formula. If the answer is no, the mean has to be the base, and that one question settles the whole choice.

Mistake 2: Dropping the absolute value

Where it slips in: The subtraction is done in whichever order the values appear, and a negative result is reported as is.

Don't do this: Report a percent difference of minus 6.9 per cent.

The correct way: Take the absolute value of the gap. A percent difference describes the size of a disagreement, so it is never negative.

Mistake 3: Calling a percent difference a percent error

Where it slips in: Both compare two numbers and both use an absolute value.

Don't do this: Use the mean as the denominator when one value is a known true value.

The correct way: Percent error divides by the true value, because the true value is authoritative. Using the mean would let a bad measurement shift the base it is being judged against.

Key Takeaways

The percent difference formula is $\frac{\lvert a - b \rvert}{(a+b)/2} \times 100$ .
The mean is the denominator precisely because neither value outranks the other.
The formula is symmetric, so the order of the two values never changes the answer.
Percent difference, percent change and percent error differ by the status of the numbers, not the arithmetic.
To work through percentages with a teacher, explore an 8th grade math tutor or math classes online.

A Practical Next Step

Find the percent difference between 18 and 22, then between 22 and 18, and confirm the two agree. Then compute the percent change in both directions and note that they do not.

Want a live Bhanzu trainer to walk through more percentage problems? Book a free demo class.

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Frequently Asked Questions

What is the percent difference formula?

\frac{\lvert a - b \rvert}{(a+b)/2} \times 100

. Divide the absolute gap between the two values by their mean, then multiply by 100.

Why does the percent difference formula divide by the mean?

Because neither value is the original, so neither has a claim to be the base. Using the mean makes the result symmetric, giving the same answer whichever value is written first.

Can a percent difference be more than 100 per cent?

Yes. When the gap exceeds the mean of the pair, as with 1 and 5, the result passes 100 per cent.

What is the difference between percent difference and percent change?

Percent change needs one value to come first and divides by that original value. Percent difference treats the two values as peers and divides by their mean.

✍️ Written By

Bhanzu Team

Content Creator and Editor

Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.

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