Percentage Difference Calculator
Two numbers, neither the start: the gap as a percentage of their average.
The calculator never sends or saves what you type.
Measuring a move from one value to another? Percentage change calculator. Comparing a result with a known correct value? Percent error calculator.
On this page
- The percentage difference formula
- How to work out percentage difference: a worked example
- Percentage difference between common pairs
- Percentage difference or percentage change?
- Percentage difference at GCSE and A level: which formula?
- When the percentage difference is over 100%
- Negative numbers and opposite signs
- The difference between two percentages
- Percentage difference in Excel or Google Sheets
- Frequently asked questions
The percentage difference formula
Difference % = |a − b| ÷ ((a + b) ÷ 2) × 100
To work out the percentage difference between two numbers, take the gap between them (subtract and drop the sign), divide it by their average (add them and halve), and multiply by 100. Neither number is the starting point, which is why the divisor is the average rather than one of the two: the answer is the same whichever number you type first. It is also called the percent difference, and labs checking duplicate samples call the same formula the relative percent difference (RPD).
It is the right measure for two values of the same kind where neither is the reference — two quotes for the same job, two readings of the same quantity, two shops’ prices for one item. If one of them is the “before” or the known correct value, you want a different formula (see below).
How to work out percentage difference: a worked example
Two builders quote £120 and £150 for the same job. How far apart are the quotes?
- Gap: |120 − 150| = 30
- Average: (120 + 150) ÷ 2 = 135
- Percentage difference: 30 ÷ 135 × 100 ≈ 22.22%
The quotes differ by 22.22% of their average — and by the same 22.22% if you list them the other way round. Type 120 and 150 into the calculator to see the same working with a check line.
Percentage difference between common pairs
The percentage difference for some pairs people look up, beside the same pair as a percentage change each way — the change depends on which number you start from; the difference does not.
| Pair | Difference | Change, first to second | Change, second to first |
|---|---|---|---|
| 20 and 30 | 40% | +50% | −33.33% |
| 50 and 100 | 66.67% | +100% | −50% |
| 75 and 100 | 28.57% | +33.33% | −25% |
| 90 and 100 | 10.53% | +11.11% | −10% |
| 25 and 75 | 100% | +200% | −66.67% |
| £1.20 and £1.50 | 22.22% | +25% | −20% |
| £500 and £600 | 18.18% | +20% | −16.67% |
| 180 and 65 | 93.88% | −63.89% | +176.92% |
Percentage difference or percentage change?
Percentage change has a direction. It measures a move from a starting value, divides by that starting value, and gives a different answer in each direction. Percentage difference has none: it divides by the average, so swapping the numbers changes nothing.
Take 40 and 60. As a difference: gap 20, average 50, so 40% in either order. As a change: 40 to 60 is +50% (20 ÷ 40), and 60 to 40 is −33.33% (−20 ÷ 60).
| Measure | Divides by | Use it when |
|---|---|---|
| Percentage difference | the average of the two | neither value is the reference |
| Percentage change | the starting value | something moved from one value to another |
| Percent error | the accepted value | one value is known to be correct |
A rule of thumb: “from X to Y” is a change; “between X and Y” is a difference. The calculator above gives both: the percentage difference as its answer, and the same pair as a change each way on the line under it. The percentage change calculator works the directional version through with its steps, and the journey link under the tool carries your two numbers across to it.
Percentage difference at GCSE and A level: which formula?
When a GCSE maths question asks for the “percentage difference” between an old value and a new one — a price before and after, a weight at birth and at six weeks — it means percentage change: the change divided by the original value. Use the percentage change calculator for those.
A level physics uses the phrase for a third thing. Pearson Edexcel’s A level Physics guidance, “Uncertainties and practical work”, works out the percentage difference between a measured 10.1 and the accepted 9.81 as (10.1 − 9.81) ÷ 9.81 × 100% = 3%, and treats under 5% as a sign of an accurate result. That divides by the accepted value, so it is percent error: the percent error calculator works it through.
For the same pair, this page’s symmetric figure is 2.91%, against percent error’s 2.96% — both 3% to one significant figure. For two close values the formulas barely differ; they part company when the values are far apart.
When the percentage difference is over 100%
It happens whenever the gap is bigger than the average. 25 and 75 differ by exactly 100% (gap 50, average 50), and the figure keeps rising as the smaller number shrinks: 0 and 50 differ by 200%, the most two numbers of the same sign can differ, because a gap of 50 is twice an average of 25. A figure near 200% therefore means one value is close to 0 relative to the other.
The calculator never rounds onto 200% unless one value really is 0: 0.001 against 1000 is 199.9996%, printed to the places it needs rather than as 200.00%. Only two numbers with opposite signs can pass 200%, and for those the formula is the wrong tool (next section).
Negative numbers and opposite signs
Two negative numbers work like two positive ones: the gap is divided by the size of their average, so −40 and −60 differ by 40%, exactly as 40 and 60 do. The calculator shows the signed average (-50) in the working and says it divided by its size.
One negative and one positive is different. Their average sits between them, close to 0 if they are similar in size, so dividing by it inflates the result: −20 and 60 give 400%. The formula assumes both values share a sign; the calculator computes the figure, prints it in plain text colour rather than green, and says so. If the two add up to exactly 0 — 50 and −50, or 0 and 0 — the average is 0 and the percentage difference is undefined.
The difference between two percentages
Between 40% and 60% there are two honest answers, and the words matter. The gap in percentage points is 20: a fixed amount, the one to use for interest rates, poll shares and pass rates. The percentage difference treats the two percentages as two numbers and gives 40% — relative to their average. Type 40 and 60 into the calculator (with or without the % sign) for the second; subtract for the first.
Percentage difference in Excel or Google Sheets
With the two numbers in A1 and B1, enter =ABS(A1-B1)/ABS(AVERAGE(A1,B1)) and format the cell as a percentage, or =ABS(A1-B1)/ABS(AVERAGE(A1,B1))*100 for a plain number. The first ABS gives the size of the gap and the second the size of the average, so the cell matches the calculator — negative numbers included — whichever cell holds which number. Fill it down to compare every pair in two columns at once.
Frequently asked questions
How do you work out the percentage difference between two numbers?
Subtract one from the other and drop the sign to get the gap, add the two numbers and halve them to get their average, then divide the gap by the average and multiply by 100. For 40 and 60 the gap is 20 and the average is 50, so the percentage difference is 20 ÷ 50 × 100 = 40%. It is the same whichever number you start with.
What is the difference between percentage difference and percentage change?
Percentage change has a direction: it measures a move from a starting value, divides by that starting value, and changes when you swap the numbers — 40 to 60 is +50%, 60 to 40 is −33.33%. Percentage difference has no direction: neither number is the reference, so it divides the gap by their average and gives 40% in either order. Use change for "from X to Y" and difference for "between X and Y".
Does it matter which number goes first?
No. The formula uses the size of the gap and the average of the two numbers, and both are the same whichever order you type them in. That is the point of percentage difference: it is for two values where neither is the starting point, such as two quotes for the same job or two measurements of the same thing.
Can the percentage difference be more than 100%?
Yes. Two positive numbers can differ by up to 200%: 25 and 75 differ by exactly 100% (a gap of 50 against an average of 50), and 0 and 50 differ by 200%, the maximum, because the gap is twice the average when one value is 0. The calculator never rounds a figure onto 200% unless one value really is 0 — 0.001 against 1000 prints 199.9996%. Only two numbers with opposite signs can go higher, and the formula is not meant for them.
Can a percentage difference be negative?
No. The gap is taken without its sign and the average by its size, so the answer is never below 0, whichever number comes first. If you worked out a negative figure, you calculated a change from the first number to the second instead — the percentage change calculator gives that, with its sign.
How do I work out the percentage difference between two percentages?
Either way works, but say which you mean. The percentage-point gap between 40% and 60% is 20 points. The percentage difference between the two percentages, treating them as two numbers, is 40% — the same formula, with 40 and 60 as the values. A percentage point is a fixed amount; a percentage difference is relative to the average of the two.
What is the percentage difference formula in Excel or Google Sheets?
With the two numbers in A1 and B1, enter =ABS(A1-B1)/ABS(AVERAGE(A1,B1)) and format the cell as a percentage, or multiply by 100 for a plain number. The first ABS takes the size of the gap and the second the size of the average, so the formula matches the calculator, negative numbers included, and gives the same answer whichever cell holds which number.
Is relative percent difference (RPD) the same thing?
Yes. Relative percent difference, the name labs use when they compare duplicate samples, is the same formula: the gap between the two results divided by their average, times 100. This calculator computes it — type the two results in either order. The acceptable RPD is set by the method or programme you work to, so check the limit there.
What is a good percentage difference?
It depends on what you are comparing; there is no general cut-off. The rule a UK student usually meets is from Pearson Edexcel’s A level Physics guidance: under 5% indicates an accurate result. That figure is measured against the accepted value, which makes it percent error rather than this symmetric formula. For two quotes or two prices, the percentage difference simply tells you how far apart they are.
What happens if one or both numbers are negative?
If both are negative the formula still works: the gap is divided by the size of their average, so −40 and −60 differ by 40%, just as 40 and 60 do. If one is negative and one positive, the average sits between them and stops being a fair yardstick — −20 and 60 give 400% — so the calculator shows the figure with a note that the formula assumes both values share a sign.
Why can’t the two numbers add up to zero?
Because their average would be 0, and nothing can be divided by 0. That happens for a positive and a negative number of the same size, and for 0 and 0. The calculator says so rather than printing an infinite or meaningless percentage; compare the gap itself instead.