A percentage difference calculator compares two values side by side by dividing the gap between them by their average: |a - b| / ((a + b) / 2) x 100. For 72 and 88 the gap is 16, the average is 80, and 16 / 80 x 100 = 20 percent.
Use it when neither number is the starting point, for example the average marks of two sections, the cut off marks of two shifts or the readings of two lab groups. If one value clearly came first and the other came later, you want percentage change instead. The section on choosing between them sets out the test in one line.
At a glance
Formula
|a - b| / ((a + b) / 2) x 100Base
Average of the two valuesSign
Always positive; order does not matterExample
72 and 88 differ by 20%Use change instead
When one value is clearly the old one
Percentage difference = |a - b| / ((a + b) / 2) x 100
a and b are the two values. The bars around a - b mean you drop any minus sign. (a + b) / 2 is their average, which acts as the shared base.
Entering two values in the tool
Type one number in each box. The order does not matter: 72 and 88 give the same answer as 88 and 72. The calculator above shows the gap, the average of the pair and the percent difference, so you can see how the answer was built.
Values can be marks, averages, counts, readings or amounts. This makes it a two value difference percentage calculator for any pair of figures you want to set side by side. Some people search for a difference in percentage calculator or a difference calculator in percentage, and they mean this same sum.
- Subtract the smaller value from the larger to get the gap.
- Add the two values and halve the total to get their average.
- Divide the gap by the average.
- Multiply by 100.
Percentage difference calculator formula explained
Gap = |a - b|
Average = (a + b) / 2
Percentage difference = gap / average x 100
Why the average? If you divided by a, the answer would change when you swapped the two numbers, and neither choice would be fairer than the other. The average sits exactly between them, so the result is the same from both sides.
Difference or change: which one to use
Ask one question: did one value come first?
- Yes, there is a before and after (last mock and this mock, old cut off and new cut off). Use percentage change, which divides the move by the earlier figure and keeps a plus or minus sign to show direction.
- No, the two are equals (Section A and Section B, Shift 1 and Shift 2, your answer and a friend's). Use percentage difference: gap over average, no sign.
Same pair, three answers. One college library holds 450 reference books and another holds 540. Going from 450 to 540 is a 20 percent increase. Going from 540 to 450 is a 16.67 percent decrease. The percentage difference, which takes no side, is 90 / 495 x 100 = 18.18 percent, sitting between the two.
A price difference percentage calculator follows the same logic: compare two shops with the difference formula, but compare one shop's old and new rate with the percentage change calculator.
Worked examples
Two sections. Section A averaged 64 in the unit test and Section B averaged 71. Gap 7, average 67.5. 7 / 67.5 x 100 = 10.37 percent.
Two lab readings. Two groups measured the same resistance as 47.2 and 49.0 ohm. Gap 1.8, average 48.1. 1.8 / 48.1 x 100 = 3.74 percent, a small gap between the two readings.
Two shifts. The highest raw score was 286 in one shift and 274 in another. Gap 12, average 280. 12 / 280 x 100 = 4.29 percent.
Table: difference and change for common pairs
The last two columns show how far apart the two measures can be. The gap grows as the values move further apart.
| A | B | Gap | Average | Difference | Change A to B |
|---|---|---|---|---|---|
| 95 | 105 | 10 | 100 | 10% | 10.53% |
| 300 | 320 | 20 | 310 | 6.45% | 6.67% |
| 50 | 60 | 10 | 55 | 18.18% | 20% |
| 72 | 88 | 16 | 80 | 20% | 22.22% |
| 90 | 110 | 20 | 100 | 20% | 22.22% |
| 80 | 100 | 20 | 90 | 22.22% | 25% |
| 200 | 250 | 50 | 225 | 22.22% | 25% |
| 60 | 90 | 30 | 75 | 40% | 50% |
| 100 | 150 | 50 | 125 | 40% | 50% |
| 10 | 30 | 20 | 20 | 100% | 200% |
The largest possible percentage difference is 200 percent, reached only when one of the two values is zero.
Mistakes people make with difference
| Slip | Effect | Fix |
|---|---|---|
| Dividing by one of the values | Answer changes when you swap them | Divide by the average of both |
| Using difference for before and after | Hides the direction of the move | Use percentage change |
| Subtracting two percentages and calling it percent | 78% vs 72% is 6 points apart | Report points, or run the formula on 72 and 78 |
| Keeping the minus sign | A negative difference has no meaning here | Take the gap as a positive number |
On the third row, 72 and 78 differ by 6 / 75 x 100 = 8 percent, which is not the same as 6 points.
Doing it in a spreadsheet and other tools
In any sheet, with the two values in C2 and D2, the cell formula is =ABS(C2-D2)/AVERAGE(C2,D2), formatted as a percent. Our guide to the percentage formula for sheets walks through it alongside marks columns. A cost difference percentage calculator, a difference amount percentage calculator and this page all run one sum, whether the pair is amounts, costs or marks. The percentage calculator hub has the other five modes, and the average percentage calculator helps when you have more than two values to compare.
Questions students ask
What is the percentage difference formula?
Take the gap between the two values, divide it by their average and multiply by 100. For 50 and 60 that is 10 / 55 x 100 = 18.18 percent.
How do I find the percentage difference between two numbers?
Subtract to get the gap, ignore any minus sign, add the two numbers and halve to get the average, then divide the gap by the average and multiply by 100.
When should I use percentage difference instead of percentage change?
Use difference when the two values are equals with no order, such as two sections or two shops. Use change when one value is the earlier one and the other is the later one.
Why does a difference percentage calculator give a different answer from a change calculator?
Difference uses the midpoint of the pair as its base, while change uses the old value. For 80 and 100 that gives 22.22 percent against 25 percent.
Can percentage difference be more than 100?
Yes, up to 200 percent. 10 and 30 differ by 100 percent, and any value compared with zero differs by 200 percent.
Is this a percentage of difference calculator for prices too?
Yes. Type the two prices in the boxes and read the percent. If the prices are an old and a new rate for the same item, use the change page instead.