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 |

× 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

× 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 =

| E₁ − E₂ |

E₁ + E₂

× 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

× 100% = 2.5%