Work out the gap and the average of your two numbers, then use What percent in the percentage calculator to see the gap as a percentage of the average. For a before-and-after change, use its % change mode instead.
Open the percentage calculatorThe percentage difference formula
Percentage difference compares two numbers when neither is the starting point. Take the gap between them, divide it by their average and multiply by 100:
Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
The bars around a − b mean “ignore the minus sign”, so the answer is always positive and it doesn’t matter which number you call a. Comparing 40 and 60 gives the same answer as comparing 60 and 40:
|40 − 60| = 20, average = (40 + 60) ÷ 2 = 50, and 20 ÷ 50 × 100 = 40%
How to calculate percentage difference, step by step
- Subtract the smaller number from the larger. For 120 and 150, the gap is 30.
- Find the average of the two. Add them and halve the result: (120 + 150) ÷ 2 = 135.
- Divide the gap by the average. 30 ÷ 135 = 0.2222.
- Multiply by 100. 0.2222 × 100 = 22.2%. The two numbers differ by about 22%.
Worked examples
| Comparing | Gap | Average | Percentage difference |
|---|---|---|---|
| 40 and 60 | 20 | 50 | 40% |
| 120 and 150 | 30 | 135 | 22.2% |
| $2.49 and $2.99 for the same item in two shops | $0.50 | $2.74 | 18.2% |
| 1,850 and 2,100 steps on two fitness trackers | 250 | 1,975 | 12.7% |
| Two quotes of $8,400 and $9,100 | $700 | $8,750 | 8.0% |
| Two readings of 9.6 and 10.0 | 0.4 | 9.8 | 4.1% |
Using the average as the yardstick is what makes the answer fair to both numbers. Neither shop and neither tracker is treated as the “right” one.
Round only at the end. For the two shop prices, rounding the average to $2.70 first gives 18.5% instead of 18.2%, a noticeable change for a small gap.
Percentage difference or percentage change?
Many people say “percentage difference” when they mean percentage change. They are different calculations and give different answers for the same pair of numbers:
| Question | Use | 120 and 150 give |
|---|---|---|
| How far apart are two comparable values? | |a − b| ÷ average × 100 | 22.2% |
| How much did a value go up from where it started? | (new − old) ÷ old × 100 | 120 to 150 is +25% |
| How much did a value go down from where it started? | (new − old) ÷ old × 100 | 150 to 120 is −20% |
Use change when there is a clear before and after: last year’s price and this year’s, your old salary and your new one. Use difference when the two numbers are side by side with no order, like two shops, two sensors or two people. The percentage increase guide covers change in depth.
In a report, say which one you used. “Shop B is 20% more expensive than shop A” and “the prices differ by 18%” can both be true of the same two prices.
“How much more” and “how much less” are different numbers
When a question names one number as the reference, such as “how much more expensive is B than A?”, it is a percentage change from that reference, and the answer depends on which way round you ask:
| Question | Working | Answer |
|---|---|---|
| How much more is 150 than 120? | 30 ÷ 120 × 100 | 25% more |
| How much less is 120 than 150? | 30 ÷ 150 × 100 | 20% less |
| How much more is $2.99 than $2.49? | 0.50 ÷ 2.49 × 100 | 20.1% more |
| How much less is $2.49 than $2.99? | 0.50 ÷ 2.99 × 100 | 16.7% less |
Both answers in each pair are correct; they just measure against different numbers. The percentage difference, 22.2% for 120 and 150, sits between them because it measures against the average. That is why it is the fairest single figure when you don’t want to favour either number.
In the percentage calculator, use % change with the reference number first for “more than” and “less than” questions.
The difference between two percentages
When both numbers are already percentages, the simplest answer is the gap in percentage points. A pass rate of 62% one year and 70% the next differs by 8 percentage points.
You can still apply either formula to the two percentages, but say so, because the results look different:
- Percentage difference: |62 − 70| ÷ 66 × 100 = 12.1%.
- Percentage change from 62% to 70%: 8 ÷ 62 × 100 = 12.9% higher.
Percent error, the science version
In a science lab you usually compare your measurement with an accepted value. That isn’t a percentage difference, because the accepted value is the reference. Divide by it instead:
Percent error = |measured − accepted| ÷ accepted × 100
Measured g = 9.6 m/s², accepted 9.81 m/s²: 0.21 ÷ 9.81 × 100 = 2.1%
If you compare two of your own measurements, neither of which is the accepted value, use the percentage difference formula with the average.
Percentage difference in Excel or Google Sheets
With the two values in A2 and B2:
| To find | Formula |
|---|---|
| Percentage difference | =ABS(A2-B2)/AVERAGE(A2,B2) |
| Percentage change from A2 to B2 | =(B2-A2)/A2 |
| Percent error, with the accepted value in B2 | =ABS(A2-B2)/B2 |
Format the result cells as percentages and the spreadsheet multiplies by 100 for you. Copy the formula down to compare a whole column of pairs.
Comparing more than two numbers
The formula only takes two values. With three or more, such as quotes from several builders or readings from several thermometers, two summaries work well:
- Spread as a percentage of the average. Take the highest minus the lowest and divide by the average of all of them. Quotes of $8,400, $8,750 and $9,100 have a spread of $700 on an average of $8,750, which is 8%.
- Each value against the average. Divide each value’s gap from the average by the average. Here $8,400 is 4% below it and $9,100 is 4% above it.
In a spreadsheet, the spread is =(MAX(A2:A10)-MIN(A2:A10))/AVERAGE(A2:A10). Say which summary you used, because the two don’t give the same number.
Checking your answer
- It sits between the two changes. For 120 and 150, the change up is 25% and the change down is 20%. The percentage difference, 22.2%, must land between them. If it doesn’t, the average is wrong.
- It never goes above 200%. An answer of 250% means you divided by something other than the average.
- Swapping the numbers changes nothing. If a and b give a different answer from b and a, you have calculated a percentage change instead.
- Close numbers give small answers. 99 and 101 differ by 2%. If two values look nearly the same but the result is large, recheck the subtraction.
Zero and negative numbers
- One number is zero. Comparing 0 and 50 gives 50 ÷ 25 × 100 = 200%. Any pair where one value is zero gives 200%, which says little, so quote the plain gap instead.
- Both are zero. The average is zero and the formula has no answer. The numbers are equal.
- Negative numbers. With one positive and one negative value, such as a profit and a loss, the average can be tiny or zero and the result is meaningless. Compare the amounts directly.
- Very different sizes. The formula can never go above 200%. For pairs like 5 and 500, a ratio (“100 times bigger”) is easier to read.
For everyday use, round the answer to one decimal place. More decimals suggest more precision than two readings or two prices usually have.