Ms. Drakoulis
Earth Science
Metric System
1
How to calculate percent error/deviation?
 Look at the front of the ESRT
 You will see a formula for calculating “percent deviation” or otherwise
called “percent error”.
The most difficult part is to figure out what is the “accepted value in a
problem” “the amount it is suppose to be” Vs the amount measured or
given. If you are able to read the problem and differentiate between those
two, then everything else is easy. You just look at your reference table and
plug in the numbers into the equation and solve the problem.
It is really simple!
Lets see why we do this:
Students often assume that each measurement that they make in the
laboratory is true and accurate. Likewise, they often assume that the
values that they derive (get) through experimentation are very accurate.
However, sources of error often prevent students from being as
accurate as they would like. Percent error calculations are used to
determine how close to the true values, or how accurate, their experimental
values really are.
The value that the student comes up with (data from an experiment or
Ms. Drakoulis
Earth Science
Metric System
2
measurement) is usually called the “observed value”, or the “experimental
value”.
A value that can be found in reference tables is usually called the true
value, or the accepted value. (That is the value that is correct! What your
measurement should be!)
The percent error can be determined when the true value is
compared to the observed value according to the equation below:
(Observed Value - True Value)
Percent Error = -------------------------------------------------- x 100%
True Value
Let's look at an example of how the formula would be used in a real-life
situation.
Ex. 1 A student measures the mass and volume of a piece of copper in the
laboratory and uses his data to calculate the density of the metal.
According to his results, the copper has a density of 8.37 g/cm3.
Curious
about the accuracy of his results, the student consults a reference table
and finds that the accepted value for the density of copper is 8.92 g/cm3.
What would be the student's percent error?
Ms. Drakoulis
Earth Science
Metric System
3
Solution - Step 1. Determine which values are known.
The students result, or the observed value = 8.37 g/cm3.
The accepted, or true value = 8.92 g/cm3.
Step 2. Substitute these values in the percent error calculation,
as shown below:
(Observed Value - True Value)
Percent Error = -------------------------------------------------- x 100%
True Value
(8.37 g/cm3 - 8.92 g/cm3)
Percent Error = -------------------------------------------- x 100%
8.92 g/cm3
Step 3. Solve for the unknown, and round to correct significant
digits.
Percent Error = -6.17%
Please note that the negative sign does not mean that the error was
less than zero, which would be impossible. It shows that the
student’s calculated value was actually too low.
Ms. Drakoulis
Earth Science
Metric System
4
Example: A student measures the volume of a 2.50-liter container to be
2.38 liters.
Ans.
What is the percent error in the student's measurement?
% error = (2.50 liters - 2.38 liters) x 100%
2.50 liters
= (.12 liters) x
100%
2.50 liters
= .048
x 100%
= 4.8% error
(Note only two sign. figs left in the answer after the subtraction)
Some for practice:
1) What is the percent difference between a measurement of the density of
aluminum, which came out be 2.9 g/cm3 and the actual value of 2.2
g/cm3?
(Ans.: 30%) (Keep only one sig. fig after the subtraction)
Compare a value of 7.428 with a value of 7.738
(Ans.: 4.17% or 4.01% depending on which you took as "actual")
(Note that you should keep three sign. figs here.)