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.
For example, if you are comparing your measured value of 10.2 m/s^{2} with the accepted value of 9.8
m/s^{2} for the acceleration due to gravity g, the percent error would be
( 2 )
percent error =
× 100% = 4%
Often, fractional or relative uncertainty is used to quantitatively express the precision of a measurement.
( 3 )
percent uncertainty =
× 100%
The percent uncertainty in this case would be
( 4 )
percent uncertainty =
× 100% = 0.39%
Comparing two experimental values
Percent difference is used when comparing two experimental results E_{1} and E_{2} that were obtained using two different methods.
( 5 )
percent difference =
× 100%
Suppose you obtained a value of 9.95 m/s^{2} for g from a second experiment. To compare this with
the result of 10.2 m/s^{2} from the first experiment, you would calculate the percent difference to be
( 6 )
percent difference =
× 100% = 2.5%