# Appendix B: Percent Error and Percent Difference

When reporting your experimental result, you will compare it to either an accepted value or an experimental value measured using a different procedure to check for consistency.

### Comparing an experimental value to a theoretical value

Percent error is used when comparing an experimental result E with a theoretical value T that is accepted as the "correct" value.
( 1 )
percent error =
 | T − E | T
× 100%
For example, if you are comparing your measured value of 10.2 m/s2 with the accepted value of 9.8 m/s2 for the acceleration due to gravity g, the percent error would be
( 2 )
percent error =
 | 9.81 − 10.2 | 9.81
× 100% = 4%
Often, fractional or relative uncertainty is used to quantitatively express the precision of a measurement.
( 3 )
percent uncertainty =
 error E
× 100%
The percent uncertainty in this case would be
( 4 )
percent uncertainty =
 0.04 10.2
× 100% = 0.39%

### Comparing two experimental values

Percent difference is used when comparing two experimental results E1 and E2 that were obtained using two different methods.
( 5 )
percent difference =
| E1E2 |
 E1 + E2 2
× 100%
Suppose you obtained a value of 9.95 m/s2 for g from a second experiment. To compare this with the result of 10.2 m/s2 from the first experiment, you would calculate the percent difference to be
( 6 )
percent difference =
| 9.95 − 10.2 |
 9.95 + 10.2 2
× 100% = 2.5%