Percent Difference Calculator

difference = |first − second| average = (first + second) ÷ 2 percent difference = |first − second| ÷ average × 100

First value

The value you are comparing: 100 in the default pair. It carries no special status — it is the first of the two only because a form has to ask for them in some order. It may be zero or negative, both of which are ordinary values here.

Second value

The other value: 150 in the default pair. Swapping the two changes nothing at all, which is the clearest sign that neither of them is the base. It is one of the two values being compared, not a reference to compare against.

Absolute difference

One value subtracted from the other, with the sign dropped: 50 for 100 and 150, and 3 for 6 and 9 where the subtraction on its own would give -3. The sign is dropped not to tidy up but because there is no fact of the matter about which value is larger — neither is more important, so the page cannot say the difference is up or down. It is the numerator of the fraction above.

Average

The two values added and halved: 125 for 100 and 150, -15 for -20 and -10. This is the base, and it is chosen because it is the only value that is neutral between the two — picking either one would make the reading depend on which you happened to treat as the reference. It is printed with its sign, so that the number on the panel is the number the division actually used: -20 and -10 divide by -15, not by 15.

Percent difference

The difference as a share of the average, times a hundred: 40% for 100 and 150, 200% for 0 and 50. It is never negative, because the absolute value covers the whole fraction and not just the numerator. It is rounded to four decimal places, which is a display width rather than a claim of precision.

The first use is a comparison between two measurements of the same kind of thing, where neither is a baseline: the heights of two people, the readings of two instruments, the price of the same item in two shops. The second is checking a percent difference someone else has quoted — the average line is the one to confirm, since it is the base that the rest of the arithmetic depends on. The third is a pair where one value is zero, which this page accepts and the percentage change pages do not, because their base is the value that would be zero. The fourth is a pair of negative values, such as two losses or two temperatures below zero, where the average is negative and the absolute value in the formula is doing real work. The fifth is a sanity check on order: if you are unsure whether you are looking at percent difference or percent change, swap the two values and recompute — percent difference gives the same answer and percent change does not.

1. 100 and 150

   1. Find the difference: 150 − 100 = 50
   2. Find the average: (100 + 150) ÷ 2 = 125
   3. Divide: 50 ÷ 125 = 0.4
   4. Multiply by 100: 40%

   The default pair, and the one that shows why the base matters. These are the same two numbers the percentage change page uses as its own default, and it reports +50% for them, because its base is the starting value 100 rather than the midpoint 125. Two pages, the same pair, two different numbers, and neither is wrong — the question being asked is different. Here the two readings on either side of the percentage are the numerator and the denominator of that fraction, so the whole calculation is checkable at a glance: 50 over 125.

2. 150 and 100

   1. Find the difference: 100 − 150 = -50, and the sign is dropped, so 50
   2. Find the average: (150 + 100) ÷ 2 = 125
   3. Divide: 50 ÷ 125 = 0.4
   4. Multiply by 100: 40%

   The pair above with the two values swapped, and every reading is identical — 40%, 50, 125. This is the property that separates percent difference from percentage change, which gives -33.3333% for the same swap rather than the same answer. The arithmetic on the way is not identical: the subtraction lands on -50 where it landed on 50 before, and the minus sign is what the absolute value removes. Both the difference and the average come out positive here because both values are positive; with two negative values the average keeps its sign, which is the case three examples down.

3. 25 and 15

   1. Find the difference: 25 − 15 = 10
   2. Find the average: (25 + 15) ÷ 2 = 20
   3. Divide: 10 ÷ 20 = 0.5
   4. Multiply by 100: 50%

   The worked example this method is usually taught with: two people's ticket sales. It is also the pair that shows why the average is the base rather than one of the values — dividing by 15 would give 66.6667% and dividing by 25 would give 40%, and nothing in the question says which of those two numbers is the reference. Choosing the midpoint removes the choice instead of making it silently, which is the whole argument for this page existing next to percentage change.

4. 0 and 50

   1. Find the difference: 50 − 0 = 50
   2. Find the average: (0 + 50) ÷ 2 = 25
   3. Divide: 50 ÷ 25 = 2
   4. Multiply by 100: 200%

   One of the two values is nothing at all, and the page accepts it: the base is the midpoint 25, which is a perfectly ordinary number, so there is no division by zero to worry about. This is the sharpest contrast with the percentage change page, where the same pair 0 and 50 has to be refused — its base is the starting value, and a percentage of zero has no value. The same is true the other way round: a difference of 200% does not mean the larger value is twice the smaller one, it means the gap is twice the midpoint. Percentages above 100% are ordinary here and mean exactly what the formula says.

5. -20 and -10

   1. Find the difference: -10 − (-20) = 10
   2. Find the average: (-20 + -10) ÷ 2 = -15
   3. Divide, and the absolute value covers the whole fraction: |10 ÷ (-15)| = 0.6667
   4. Multiply by 100: 66.6667%

   Both values are negative, such as two temperatures below zero or a loss in each of two years. The average comes out as -15 and is printed that way, because the number on the panel has to be the number the division used — printing 15 while dividing by -15 would leave the reader with nothing to check against. The percentage is still positive, since the absolute value is outside the whole fraction rather than only around the numerator: without it this pair would report -66.6667% for two values that are simply 10 apart.

The base here is the average of the two values, and that is a choice rather than a fact. It is made because neither value is the reference: divide by either one instead and you get a different answer for the same pair — for 25 and 15, dividing by 15 gives 66.6667% and dividing by 25 gives 40%. The average is the only base that treats the two as equals, but it is not more correct than the others, it just answers a different question. If what you have is an old value and a new value, the question you are asking is percentage change rather than percent difference, and its base is the old value; if you have an approximate value and an exact one, it is percentage error with the exact value as the base. The same pair 100 and 150 is 40% here and +50% on the percentage change page, and both figures are right. One input is refused: when the two values are exact opposites, such as 50 and -50, the average is zero and the division has no answer, and the page says so rather than returning a number. Two values of zero are refused for the same reason. Zero on its own is fine, and so are two negative values — 0 and 50 gives 200%, and -20 and -10 gives 66.6667%. Values that very nearly cancel each other are also accepted, and the reading becomes very large as the average approaches zero; a pair like 0.00001 and -0.000009 gives a percentage in the thousands while the average prints as 0.0000 at four places. That is the formula behaving as written rather than a defect, and no second guard has been added for it, because a rule that refused values near zero would be a threshold, and a threshold is a product decision rather than an arithmetic fact. This page makes no judgement about size: it does not say whether 5% is a lot, because that depends entirely on what is being measured — a 5% difference in two people's heights is unremarkable and a 5% difference between two instrument readings may be a great deal. All three readings are rounded to four decimal places, and this page does not round for you beyond that: a source that prints 31.9% for 160 and 116 is rounding to one place, while this page prints 31.8841% for the same pair. None of the three readings carries a unit, since the two inputs may be heights, temperatures, sales or headcounts and all three outputs are a ratio or an average of them.

How do you calculate percent difference?

Take the difference between the two values and divide it by their average, then multiply by 100. For 100 and 150 the difference is 50 and the average is 125, so the percent difference is 40%. Drop any minus sign on the difference before dividing — the formula is 50 over 125, not -50 over 125.

Why divide by the average instead of one of the two values?

Because neither value is the reference. Dividing 10 by 15 gives 66.6667% and dividing it by 25 gives 40%, and the question does not say which of the two should be the base. Using the midpoint removes that choice: it is the only base that treats the two values as equally important, so the answer does not depend on which one you happened to list first.

What is the difference between percent difference and percent change?

The base. Percent difference divides by the average of the two values, because neither is a reference; percentage change divides by the old value, because there is one. The same pair 100 and 150 gives 40% here and +50% there, and both are correct — they answer different questions. If there is an old value and a new value, use percentage change.

Does the order of the two values matter?

No. 100 and 150 give 40%, and 150 and 100 give 40% as well, with the difference and the average identical too. Swapping them only changes the sign of the subtraction underneath, which is exactly what the absolute value is there to remove. Percent change behaves the other way: swap its two values and the answer changes.

Can I use zero or negative values?

Yes to both. 0 and 50 gives 200%, since the average is 25 and the division is perfectly ordinary — this is where percent difference parts company with percent change, which refuses a starting value of zero. -20 and -10 gives 66.6667%, with the average printed as -15. The only pair that cannot be answered is two values that cancel exactly, such as 50 and -50, because the average is then zero.

Is a large percent difference a problem?

This page has no opinion, and deliberately so. What counts as a large difference depends on what you are measuring — 5% between two people's heights is nothing, and 5% between two instrument readings can be a great deal. The page reports the number and stops there; there is no threshold, no band and no verdict attached to it.

• Percent Difference — the method on this page: the two values are equally important and neither is a reference, so the comparison uses their average; includes the worked examples 25 and 15, 6 and 9, 4 and 6, 160 and 116, and the note that the answer does not depend on which value is listed first — Maths Is Fun (Rod Pierce)
• Absolute Difference — the absolute value of one number minus another, which is the numerator of the fraction on this page and the reason the reading is never negative — Wolfram MathWorld (United States)
• Percentage Change — the neighbouring convention, which measures against the initial value instead of the average and is therefore not symmetric when the two are reversed — Wolfram MathWorld (United States)
• Percent — a number expressed as a fraction of one hundred, which is the form the main reading on this page is printed in — Wolfram MathWorld (United States)