Percentages
Percent Difference vs Percent Change
Percent change measures how far a value moved from a starting point, so it has a direction and uses the old value as its base. Percent difference compares two values with no starting point, so it divides by their average and is the same either way round. For 40 and 50, the percent difference is about 22.22%, while the percent change is +25% one way and −20% the other.
Percent difference or percent change: which one?
Ask one question: is one of the two numbers the starting point?
- Yes, there is a before and an after (last year and this year, the old price and the new price): use percent change. The before value is the base.
- No, the two values are peers (two stores’ prices on the same day, two repeat measurements, two candidates’ test scores): use percent difference. Neither value is privileged, so the base is their average.
- One value is the correct or accepted one (a measurement against a textbook value): use percent error, which divides by the accepted value.
The three formulas share the same top line, the gap between the values. They differ only in what they divide by, and that single choice is why the answers differ. The percentage difference calculator shows the percent difference and both percent changes side by side, which makes the contrast easy to see.
The percent difference formula
The vertical bars mean absolute value: drop any minus sign, so the gap is always positive. The absolute value calculator covers the notation if it is unfamiliar. The bottom line is the ordinary mean of the two values, the same one the average calculator gives. Dividing by the average puts both values on an equal footing, which is the whole point. Swap a and b and nothing changes.
Example: percent difference between 40 and 50
The average of 45 sits between the two values, so the result, about 22.22%, falls between the two percent changes of 25% and 20%.
Percent difference never carries a sign. It tells you how far apart two values are, not which is larger. If the direction matters, say it in words (“B is higher by about 22.22%”), or switch to percent change.
The percent change formula
Percent change keeps the sign and divides by the starting value. That makes it depend on the order. Going from 40 to 50 and from 50 to 40 are different moves, with different answers.
The two answers are not mirror images because the base changes. A 10-point move is a quarter of 40 but only a fifth of 50. This asymmetry is covered in more depth in the percentage increase formula guide, and the percentage change calculator works it out with the sign and the word increase or decrease.
Worked examples
Example: two stores, same product
A gallon of milk is $3.40 at one store and $3.65 at another, on the same day. Neither price came first, so this is a percent difference.
If you instead say “the second store is 7.35% more expensive,” you have used the first store as the base: 0.25 ÷ 3.40 ≈ 7.35%. That is fine as long as you state the base, but it is a percent change, not a percent difference.
Example: two repeat measurements
A length is measured twice, giving 9.8 cm and 10.2 cm. Labs often report how well repeat readings agree as a percent difference.
Percent change would give about 4.08% one way and about −3.92% the other, which makes no sense when neither reading is the original.
Example: sales growth
Monthly sales went from 1,200 units to 1,500 units. There is a clear before and after.
Reporting this as a percent difference, about 22.22%, would understate the growth and hide its direction.
Example: a measurement against a known value
An experiment measures gravity as 9.6 m/s² against an accepted 9.81 m/s².
The accepted value is the base because it is the reference. The percent error calculator gives this along with the signed error.
Why the answers differ, and by how much
For values that are close together, all three measures nearly agree. As the gap grows, they pull apart, because the average, the smaller value and the larger value drift further from each other.
| Values | Percent difference | Change, low → high | Change, high → low |
|---|---|---|---|
| 100 and 101 | ≈ 0.995% | +1% | ≈ −0.99% |
| 90 and 100 | ≈ 10.53% | ≈ +11.11% | −10% |
| 40 and 50 | ≈ 22.22% | +25% | −20% |
| 60 and 80 | ≈ 28.57% | ≈ +33.33% | −25% |
| 250 and 400 | ≈ 46.15% | +60% | −37.5% |
| 50 and 100 | ≈ 66.67% | +100% | −50% |
| 10 and 30 | 100% | +200% | ≈ −66.67% |
| 1,000 and 10,000 | ≈ 163.64% | +900% | −90% |
Two patterns are worth noticing. First, the percent difference always lands between the size of the two percent changes, because its base, the average, lies between the two possible bases. Second, only the ratio of the two values matters, not their size: 50 and 100 give the same figures as 100 and 200, and 10 and 30 give the same as 1 and 3. Scaling both values by the same factor cancels out of every formula.
A falling percent change can never go below −100%, but a rising one has no ceiling. Percent difference behaves differently again: it tops out at 200%, reached when one value is zero. That cap is why percent difference is a poor choice for describing big growth. “Up 900%” tells a reader much more than “a percent difference of about 163.64%.”
Zeros, negatives and other definitions
When one value is zero. Percent change from zero is undefined, since you cannot divide by zero; there is no percentage that describes growing from nothing. Percent difference between 0 and any positive number is 200%, whatever that number is, so it carries no information about size. If both values are zero, percent difference is undefined too.
When the values have opposite signs. Comparing −10 and 10 puts zero in the denominator of the percent difference formula, because their average is 0. Even when the average is not zero, mixing signs gives results that are hard to read. For profit and loss figures or temperatures that cross zero, report the plain gap rather than a percentage.
Other definitions. “Percent difference” is not used consistently outside math classes. Some fields divide by the larger value, some by the smaller one, and some use it loosely to mean percent change. The average-based formula on this page is the one most textbooks call percent difference and the one this site’s calculator uses. If a source does not say which base it used, check before comparing its figures with yours.
Common mistakes
- Using percent difference for growth. Before-and-after data needs percent change. Percent difference hides the direction and caps at 200%.
- Using percent change for two peers. The answer then depends on which value you happened to list first.
- Dividing by the sum instead of the average. 10 ÷ 90 gives about 11.11%, half the correct 22.22% for 40 and 50. Halve the sum first.
- Expecting percent changes to reverse. +25% then −20% gets back to the start; +25% then −25% does not.
- Not stating the base. “7.35% more expensive” and “a 7.09% difference” are both right for $3.40 and $3.65. Say which you used.
- Calling a points gap a percent difference. From 40% to 50% is 10 points, a 25% increase, and a percent difference of about 22.22%.
Every one of these is a question of the base. The general rule from how to calculate percentage applies: a percentage is always a part divided by a whole, and the whole has to be the right one. The what percent of calculator lets you choose the base explicitly when you need a figure other than these three.
Frequently asked questions
What is the percent difference formula?
Percent difference equals the absolute difference between two values divided by their average, times 100: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50, that is 10 ÷ 45 × 100 ≈ 22.22%. The result is the same whichever value you put first, and it never has a sign.
What is the difference between percent difference and percent change?
Percent change divides the gap by the starting value and keeps the sign, so it describes a move from old to new. Percent difference divides the gap by the average of the two values and has no sign, so it compares two peers. For 40 and 50, the change is +25% or −20%; the difference is about 22.22%.
What is the percent difference between 40 and 50?
About 22.22%. The gap is 10 and the average is 45, so 10 ÷ 45 × 100 ≈ 22.22%. For comparison, going from 40 to 50 is a 25% increase, and going from 50 to 40 is a 20% decrease. The percent difference always sits between those two figures.
When should I use percent difference?
Use it when neither value is a starting point or a reference: two stores’ prices, two repeat measurements, two products’ ratings. If there is a before and after, use percent change. If one value is the accepted or correct value, use percent error, which divides by that accepted value.
Can percent difference be more than 100%?
Yes, up to a maximum of 200%. Values of 10 and 30 have a percent difference of exactly 100%, and 1,000 and 10,000 give about 163.64%. The 200% ceiling is reached when one value is zero. Percent change has no ceiling on increases, which is why it suits growth figures better.
Is percent difference the same as percent error?
No. Percent error divides the gap by an accepted or true value, while percent difference divides by the average of two measured values. A measurement of 9.6 against an accepted 9.81 has a percent error of about 2.14%. Two readings of 9.8 and 10.2 have a percent difference of 4%.
Why is the percent change from 50 to 40 not −25%?
Because percent change divides by the starting value. From 50 to 40, the drop of 10 is divided by 50, giving −20%. From 40 to 50, the same 10 is divided by 40, giving +25%. Different bases give different percentages even though the gap is identical.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/percent-difference-vs-percent-change/