Percent error is the percentage difference between a known or Actual Value and a Measured Value or calculated value. It indicates the accuracy of measurement. The smaller the percent error, the more accurate the result is.
δ = Percent Error
VA = Actual value or Exact value
VE = Expected value or Measured value
δ = | VA - VE |/VA × 100%
If we want to make the equation more meaningful and less confusing, then we can use the formula as follows:
Percent Error = | Actual Value - Measured Value |/Actual Value× 100
Now we will learn how to calculate percent error using the percent error formula as we mentioned above.
So here is a problem to solve based on the values we have and using the percent error formula.
Let's say that you have an experiment and you are measuring the density of aluminum. Let's say your measured value of aluminum is 2.5 grams per cubic centimeter and, we know that the accepted value or the actual density of aluminum is 2.7 grams per cubic centimeter.
So based on the above values, what is the percent error in this experiment?
As we already have all the values and the formula we need to calculate percent error in this problem, we can arrange them as follows:
% Error = | Actual Value - Measured Value |/Actual Value× 100
= | 2.7 - 2.5 |/2.7× 100
= | 0.2 |/2.7× 100
= 0.2/2.7× 100
= 0.074 × 100
So we got 7.4% and this is the percent error for this experiment.
Question: In a class of thirty students, 23 students passed an exam, whereas the remaining seven did not. While publishing the marks, the teacher makes a mistake and lists 25 students who passed and five students who failed the exam. So, what is the percentage error in the number of students who passed the exam?
Answer: 8.695% is the percentage error in the number of students who passed the exam.