Enter two numbers and get the percentage difference between them, with every step shown. This is the right tool when neither number is the starting point, like two lab readings or two prices from different shops.
Enter the numbers
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Your answer
Your answer shows up here once you fill in both numbers.
What to enter
- First number and second number
- Any two numbers. Neither one is the "old" or the "new" one, so you can enter them in either order.
Worked examples
Two lab readings
Two groups measured the same sample and got 50 and 60. How far apart are they, as a percent?
- Find the difference, ignoring the sign: |50 – 60| = 10.
- Find the average of the two numbers: (50 + 60) ÷ 2 = 55.
- Divide the difference by the average: 10 ÷ 55 = 0.181818.
- Multiply by 100: 0.181818 × 100 = 18.181818%.
The two readings are 18.181818% apart. Swap them and you get the same answer, because the average of the two numbers is the base.
Two prices
One shop sells a textbook for 120 and another for 80. What is the percentage difference?
- Find the difference, ignoring the sign: |120 – 80| = 40.
- Find the average of the two numbers: (120 + 80) ÷ 2 = 100.
- Divide the difference by the average: 40 ÷ 100 = 0.4.
- Multiply by 100: 0.4 × 100 = 40%.
The prices differ by 40%. That is bigger than 33.33%, which is how much cheaper 80 is than 120, because the base here is the average of the two prices.
Percentage difference or percentage change?
Percentage change starts from an old number, so the order matters. Percentage difference has no starting point, so the order does not. This table shows the same pairs both ways.
| Pair | Percentage change | Percentage difference |
|---|---|---|
| 50 to 60 | 20% | 18.1818% |
| 60 to 50 | -16.6667% | 18.1818% |
| 100 to 150 | 50% | 40% |
| 150 to 100 | -33.3333% | 40% |
Use percentage change when something happened over time, like a grade going up or a price falling. Use percentage difference when you compare two things side by side and neither came first.
How big can the answer be?
For two positive numbers, the answer never goes above 200%. If one number is 0 and the other is 40, the difference is 40 and the average is 20, so the answer is 200%. The answer is 0% when the two numbers are equal.
How it is calculated
- Subtract one number from the other and ignore the sign. This is the difference.
- Add the two numbers and divide by 2. This is the average.
- Divide the difference by the average.
- Multiply by 100 to turn it into a percent.
Percentage difference = |a – b| ÷ ((a + b) ÷ 2) × 100
Assumptions to keep in mind
- The base is the average of the two numbers. Some textbooks use the larger number or one of the two numbers as the base. If your course does, use the percentage change mode on the percentage change calculator instead.
- If the two numbers average to 0, for example -5 and 5, the page asks you to use the plain difference, because you cannot divide by 0.
- This page does the arithmetic only. It does not know whether the difference matters.
Mistakes that give the wrong answer
Using percentage change for two readings
Percentage change picks one number as the start. Two readings from the same experiment have no start, so the percentage difference is fairer.
Dividing by one of the numbers
The base is the average of both numbers. Dividing by just one gives a different answer.
Forgetting the absolute value
The difference is always positive here. If you get a negative answer by hand, you subtracted in the order that made it negative. Drop the sign.
Mixing up percent and percentage points
If you compare two rates, like 4% and 6%, the gap between them is 2 percentage points. The percentage difference between the two rates is 40%. Say which one you mean.
Questions students ask
How do I calculate percentage difference?
Find the difference between the two numbers, divide it by their average, then multiply by 100. For 50 and 60, that is 10 ÷ 55 × 100 = 18.18%. The calculator shows each step.
What is the difference between percentage difference and percentage change?
Percentage change starts from an old number and measures how much it moved. Percentage difference compares two numbers with no starting point and uses their average as the base. The table on this page shows both for the same pairs.
Does the order of the numbers matter?
No. The difference ignores the sign and the average is the same either way, so the answer does not change.
Why use the average as the base?
Because neither number is more important than the other. Using the average treats them equally.
Can the percentage difference be more than 100%?
Yes. For two positive numbers, it can reach 200%. If one number is more than three times the other, the answer goes above 100%.
