Percent Error
When we do an experiment in physics or science, there is always some possibility of
error. This error can come from several sources: the limitations of the tools we are using
to measure, extraneous (outside) forces . Of course some errors are the result of less
than careful work.. Whatever the cause, errors occur. The important part is that we can
measure the extent of the error. Often the amount of error suggests a new way of
looking at what is going on with the experiment.
The general formula for % error is
accepted ! measured
" 100
accepted
The vertical bars mean “absolute value.” Generally, %error is a positive number.
The accepted value is the value you should get. It might be listed in a book. For
example, when we measured the rpm’s of the drill using the strobe light, we compared
them to the manufacturer’s values printed inside the drill housing. The manufacturer’s
numbers were the accepted values and our measurements were the measured values.
Example: When using number three pulleys on the both the motor and the drive of the
drill, we measured the drill rate to be 1700 rpm. The accepted value (from the
manufacturer) was 1600 rpm. What was our % error?
Accepted = 1600 rpm
measured = 1700 rpm
Put it in the calculator like this ((1600-1700)/1600) X 100
You should get -6.25%
Don’t keep the negative sign
Instead of an accepted value, we might get a theoretical value. The theoretical value
would be the result of a calculation we do knowing the laws of physics. For example, if
we were to let a hot wheels car roll down a ramp, we might calculate that its velocity at
the bottom of the ramp (using Newton’s laws and the measured acceleration due to
gravity) should be 2.54 meters/second. This would be the theoretical value. It didn’t
come straight from a book. We might measure the car’s velocity to be 2.48 m/s.
Theoretical value: 2.54 m/s
Measured value: 2.48 m/s
theoretical ! measured
" 100
theoretical
((2.54-2.48)/2.54) X 100 = 2.36% error
For the following accepted values and measured values for drill rpm’s, calculate the %
error
You will often be programming a spreadsheet program to calculate the percent error.
The formula that you will enterwill look like this.
You must be careful how you insert
parentheses. It is the most common
mistakes in writing spreadsheet programs
= abs((e2-f2)/e2)
You always need the =
sign, that tells the
program to do a math
operation
e2 and f2 refer to the cells of the
abs is abbreviation for spreadsheet in which the data to be
absolute value on all
operated on is placed. When you copy
spreadsheet programs
and paste a spreadsheet formula, the
program knows to adjust the cell
numbers and letters appropriately. In
this case, e2 contains the theoretical or
accepted value and f2 contains the
measured value
Determine the percent error for the following theoretical and measured velocities of a
hot wheels car.
A
1
B
theoretical
C
measured
% error
2
2.54
2.36
3
3.00
3.25
4
4.50
4.55
5
3.22
3.22
6
9.86
9.75
7
10.00
6.25
8
12.50
12.49
9
3.75
3.55
10
4.50
4.25