Percentage Difference & Percent Error Calculator
- Absolute difference
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- Change from first to second
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- Change from second to first
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Checked against: 40 and 60: percentage difference 40%; measured 9.6 against a true 9.81: percent error 2.14% Last reviewed:
Sources and method
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Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100. For 40 and 60 that is 20 ÷ 50 × 100 = 40%. Percent error compares a measurement with a true value instead: |measured − true| ÷ |true| × 100.
“Percentage difference”, “percentage change” and “percent error” sound interchangeable, but they answer different questions and give different numbers for the same pair of values. This calculator covers the two that are not about growth. For a before-and-after change, use the percentage calculator.
Percentage difference
Use it when you are comparing two values and neither one is the reference: two quotes for the same job, two lab readings, the population of two towns.
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Dividing by the average treats both numbers fairly, so the answer is the same whichever value you call A. Two plumbers quote 400 and 460: the difference is 60, the average 430, so the quotes are 60 ÷ 430 × 100 = 13.95% apart.
Percent error
Use it when one of the values is known to be correct, typically in science and engineering:
Percent error = |Measured − True| ÷ |True| × 100
A student times a pendulum and calculates g = 9.6 m/s². The accepted value is 9.81. The error is 0.21, and 0.21 ÷ 9.81 × 100 = 2.14%. The measurement was low, so the signed error is −2.14%.
Percent error is a percentage change measured from the true value, with the sign usually dropped.
Difference, change and error compared
| Values | Percentage difference | Change, first to second | Change, second to first |
|---|---|---|---|
| 40 and 60 | 40.00% | +50.00% | −33.33% |
| 50 and 55 | 9.52% | +10.00% | −9.09% |
| 100 and 150 | 40.00% | +50.00% | −33.33% |
| 80 and 120 | 40.00% | +50.00% | −33.33% |
| 10 and 30 | 100.00% | +200.00% | −66.67% |
| 200 and 100 | 66.67% | −50.00% | +100.00% |
The table shows the key property: percentage change is asymmetric (40 to 60 is +50%, but 60 to 40 is −33.33%), while percentage difference is not. That is exactly why percentage difference is the right tool when there is no “before” and “after”.
Which one to use
- There is a starting value and a new value (prices over time, last year’s sales): percentage change.
- There is a correct or expected value (lab results, estimates against actuals): percent error.
- The two values are peers (two products, two methods, two measurements): percentage difference.
- The values are themselves percentages (interest rates, pass rates): consider the difference in percentage points instead, explained in our guide to percentage points.
Common mistakes
- Dividing by one of the values for a percentage difference. That turns it into a percentage change with an arbitrary direction.
- Dividing by the measured value in percent error. The base is always the true value.
- Using percentage difference near zero. When the two values have opposite signs or an average close to zero, the result blows up and stops meaning much. Report the absolute difference instead.
- Reporting too many decimals. A percent error can be no more precise than the measurements behind it.
Frequently asked questions
How do I calculate the percentage difference between two numbers?
Divide the absolute difference by the average of the two numbers and multiply by 100. For 40 and 60: the difference is 20, the average is 50, and 20 ÷ 50 × 100 = 40%.
What is the difference between percentage difference and percentage change?
Percentage change measures from a starting value, so it has a direction: 40 to 60 is +50%, and 60 to 40 is −33.3%. Percentage difference compares two values as equals, using their average as the base, so 40 and 60 are 40% apart whichever way round you put them.
How do I calculate percent error?
Percent error = |measured − true| ÷ |true| × 100. Measuring g as 9.6 m/s² against the accepted 9.81 gives 0.21 ÷ 9.81 × 100 = 2.14%.
Can percent error be negative?
The usual definition takes the absolute value, so percent error is never negative. Some lab courses keep the sign to show whether the measurement was too high or too low. The calculator shows both: the absolute error as the result, and the signed figure underneath.
When should I use percentage difference rather than percentage change?
Use percentage change when one value is clearly the starting point, such as last year versus this year. Use percentage difference when neither value is a reference, such as two shops’ prices or two lab measurements.
What is a good percent error?
It depends entirely on the experiment. School lab work often treats under 5% as good and under 10% as acceptable, while precision measurements may need far less than 1%. Your instructor or the method’s stated uncertainty is the right benchmark.