Error Calculations
Where there is an accepted value for a quantity which you are determining in an experiment, you should
include a calculation of the absolute error and the relative error in the experiment. For instance, let’s
say the slope of a velocity vs. time graph represents the acceleration due to gravity, and the accepted
value for this quantity is 9.80 m/s2. The slope of your velocity vs. time graph yields an experimental of
9.92 m/s2. Make sure that you describe how you determined the experimental and accepted values, The
calculation of the absolute error and relative error would be as follows:
Experimental Value = slope of velocity vs. time graph
Experimental Value = 9.92 m/s2
Accepted Value = acceleration due to gravity on earth
Accepted Value = 9.80 m/s2 (Determined from Hewitt textbook, Conceptual Physics, page 18.)
ABSOLUTE ERROR
Absolute Error = accepted value - experimental value
m
s2
Absolute Error = 9.80
Absolute Error = -0.12
Absolute Error = 12
! 9.92
m
s2
m
s2
m
s2
RELATIVE ERROR
Absolute Error
Relative Error =
Accepted Value
Relative Error =
0.12
9.80
m
s2
m
s2
Relative Error = 0.012
Relative Error = 1.2%
So, how would this look for the toy car experiment? What would be your accepted value? What would be
your experimental value? In this experiment, you were limited by the fairly primitive tools you used to
measure position and clock reading. On the other hand, the computer with the motion detector was able to
collect a large number of data points with fairly high precision. Consequently, we will take as the accepted
value of the speed of the car, the value of the slope of the computer generated position vs. time graph. Since
our experiment was done using the flasher and the tiles in the hallway, the slope of the position vs. time
graph from that experiment will be our experimental value. Assume the slope of the computer generated
graph is 0.329 m/s. Assume the slope of your hallway experiment is 0.34 m/s. The error calculation for this
experiment would therefore look like the one shown on the next page.