Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Percent error measures how far an experimental result strayed from an accepted or theoretical value, and it's calculated against the theoretical value specifically as the base, not the experimental one, which matters because dividing by the wrong one of the two numbers changes the resulting percentage.
Before you rely on it
What to check
Confirm which of the two values is the accepted theoretical figure before running the calculation, since that one belongs in the denominator, not the experimental result.
The common error
Where people go wrong with percent error calculator
Dividing by the experimental value instead of the theoretical one. The formula is specifically built around the accepted value as the reference point, and swapping the two changes the resulting percentage.
Sensitivity evidence
How experimental value changes the percent error
| Experimental value | Percent error | Absolute error |
|---|---|---|
| 8 | 18.4% | 1.8 |
| 9 | 8.2% | 0.8 |
| 10 | 2.0% | 0.2 |
| 11 | 12.2% | 1.2 |
| 12 | 22.4% | 2.2 |
Every input, tested
Which input moves the percent error most
| Input | Tested from | To | Percent error at each end | Swing |
|---|---|---|---|---|
| Theoretical value | 9 | 11 | 7.8% to 11.8% | 4.0% (396%) |
| Experimental value | 9 | 11 | 8.2% to 12.2% | 4.1% (400%) |
Two variables at once
Percent error by experimental value and theoretical value
| Experimental value \ Theoretical value | 8 | 10 | 12 |
|---|---|---|---|
| 8 | 0.000% | 20.0% | 33.3% |
| 9 | 12.5% | 10.0% | 25.0% |
| 10 | 25.0% | 0.000% | 16.7% |
| 11 | 37.5% | 10.0% | 8.3% |
| 12 | 50.0% | 20.0% | 0.000% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Experimental value | 9.7 |
| Theoretical value | 9.8 |
| Percent error | 1.0% |
| Absolute error | 0.1 |
Where the inputs come from
Enter the experimental value, the number you measured or estimated, and the theoretical value, the accepted or expected number. The theoretical value must not be zero, since the error is measured relative to it. Use the same units for both, and take the theoretical value from a reliable source such as a physics table or a known standard. Do not round the values before entering them.
When the result stops applying
The absolute value means percent error does not show whether you were too high or too low, so report the sign separately if it matters. It is not the same as percent difference, which compares two measured values with no accepted reference. For small theoretical values, small absolute errors give large percentages.
What to compare it with
Compare two measurements with no true value on the percent difference calculator, and see the percentage change page for growth between values. The mean and standard deviation calculators measure repeatability, and the rounding page shows the effect of precision. The physics calculators provide accepted values for many constants.
People also ask
Frequently asked questions
What is the formula for percent error?
Take the absolute difference between the experimental and theoretical values, divide by the theoretical value and multiply by 100.
What is a good percent error?
It depends on the setting. In introductory labs under 5% is often acceptable, and precision work requires much less.
How is percent error different from percent difference?
Percent error compares a measurement with a known accepted value, while percent difference compares two values with no reference.