Percent Error
Percentage error is a measurement of the discrepancy between an observed and a true or accepted value. While measuring data, the result often varies from the true value. The error can arise due to many different reasons that are often related to human error but can also be due to estimations and limitations of devices used in the measurement. Regardless, in such cases , it becomes important to calculate the percentage error. The computation of percentage error involves the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error multiplied by 100 to obtain the percentage error. Refer to the equations below for clarification.
Absolute error = \(V_{\text{true}}V_{\text{observed}}\)
\(\text {Percent Error} = \left  \dfrac{\text {Actual Value  Estimated Value}}{\text {Actual Value}}\right \times 100\)
1.  What is Meant by Percent Error? 
2.  Percent Error Formula 
3.  How do you find the Percent Error? 
4.  Solved Examples on Percent Error 
5.  Practice Questions on Percent Error 
6.  FAQs on Percent Error 
What is Meant by Percent Error?
Whenever an experiment is done, we get results that will match with the actual value or sometimes vary with the actual value. Error is the difference between the estimated value and the actual value. Measurement errors arise because of unavoidable faults in the measuring instrument and limitations of the human eye. Errors come in all sizes, and sometimes we need to decide if the error in our measurement is so big that it makes the measurement useless. The smaller the error indicates that we are close to the actual value. Therefore, scientists have devised a method to calculate the extent of error in estimation.
Percent Error Definition
Percent error is the difference between the actual value and the estimated value compared to the actual value and is expressed in a percentage format. In other words, you find the difference between the actual answer and the guessed answer, divide it by the actual answer, and express it as a percentage. Percent errors indicate how huge our errors are when we measure something. For example, a 5% error indicates that we got very close to the accepted value, while 60% means that we were quite far from the actual value.
Percent Error Formula
Percent error will let us know how much extent these unavoidable errors affect our experimental results. The formula for finding percent error:
\(\text {Percent Error} = \left  \dfrac{\text {Actual Value  Estimated Value}}{\text {Actual Value}}\right \times 100\)
Most of the time, the percentage error is expressed as a positive value. Absolute value can be some times termed as true value or theoretical value. The absolute value of the error is divided by an true value and shown as a percent.
Think Tank
 The accepted distance to the moon is 238,855 miles on a particular day. You measure the distance as 249,200 miles. What is the percent error?
 Ron is planning a hiking trip, and he estimated the gradient of the trail to be 210 ft/mile. After hiking and tracking the trail, he found that the trail was actually 202 ft/mile. What was his percent error? Did he overestimate or underestimate the gradient?
How do you Find the Percent Error?
Percentage error can be calculated using three simple steps:
 Calculate the error (subtract estimated value from the actual value) ignore any negative () sign. i.e., take the absolute value of error.
Absolute Error = Approximate Value – Exact Value
 Divide the error by the actual value (sometimes, we may get a decimal number).
Relative Error = Approximate Value – Exact Value/Exact Value
 Convert that to a percentage (by multiplying by 100 attach "%" sign)
Percent Error = Approximate Value – Exact Value/Exact Value × 100%
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Important Notes

Percent error is the difference between the actual value and the estimated value compared to the actual value and is expressed in a percentage format.

Percent Error = {(Actual Value  Estimated Value)/Actual Value} × 100

Percent errors indicate how huge our errors are when we measure something.
Solved Examples on Percent Error

Example 1: John measured his height and found 5 feet. But later on, by careful observation, he has found his actual height to be 4.5 ft. Find the percent error he made in measuring his height.
Solution:
Before solving the problem, let us identify the information: Actual value: 4.5 ft and Estimated value: 5 ft.
Now,
Step1: Subtract one value from others to get the absolute value of error.
Error = 4.5 − 5 = 0.5
Step2: Divide the error by actual value.
0.5/4.5 = 0.1111 (up to 4 decimal places)
Step3: Multiply that answer by 100 and attach the % symbol to express the answer as a percentage.
0.111 × 100 = 11.11
Percentage error = 11.11%

Example 2: Harry got a traffic penalty notice for police speeding for traveling 70 mph in a 60 mph zone. Harry claimed his speedometer said 60 mph, not 70 mph. What could Harry claim as his percent error?
Solution:
Let us arrive at %error in 3 steps:
Absolute Error = 70−60 = 10
Percent Error = 10/60=0.1667
= 0.1667×100 = 16.67%
Harry can claim 16.67% as his percent error

Example 3: Helen's math class had 24 students yesterday. She miscounted the class total and recorded it as 18 students. What is Helen's percent error?
Solution:
The actual number of students: 24 and Recorded number of students: 18
Absolute Error = 24  18 = 6
Percent Error = 6/24 = 0.25
= 0.25 × 100 = 25%
Helen's percent error is 25%

Example 4: The Handbook of Chemistry and Physics lists the density of a certain liquid to be 0.7988 units. Daniel experimentally finds this liquid to have a density of 0.7925 units. The teacher allows up to +/ 0.500% error to make an “A” in the lab. Did Daniel make an “A”? Prove your answer.
Solution:
Given, Theoretical value of density of a liquid: 0.7988 units and Daniel's Experimental value of the density: 0.7925 units
Percent Error = {(Actual Value  Estimated Value)/Actual Value} × 100
% Error = (0.7988−0.7925)/0.7988 × 100
= 0.0063/0.7988 × 100
= 0.788%
Daniel got a 0.788% error. But, the teacher allows only a 0.5% error.
So, Daniel could not make an "A".
FAQs on Percent Error
Can you have a Negative Percent Error?
If the experimental value is less than the accepted value, then the percent error is negative. Generally, the error is calculated as the absolute difference to avoid the confusion of a negative error.
What does a Percent Error tell you?
Percent error tells us how much extent few unavoidable errors affect our experimental results. It is measured by taking the difference between the actual value and the observed value. Small percent errors indicate that you are close to the accepted or real value.
Percent errors tell how big your errors are when you measure something in an experiment.
Is High Percent Error Good or Bad?
A 5% error indicates that we got very close to the accepted value, while 60% means that we were quite far from the actual value. So, a high percent error is bad.
How do you Decrease the Percent Error?
By increasing accuracy, precision and taking the measurements under controlled conditions, we can decrease the percent error.
What is the Difference Between Percent Error and Percent Difference?
Percentage difference is the measurement of the percentage change in the initial and final quantities in an experiment, while percent error shows us the measurement of the discrepancy between an observed and a true or accepted value.
The percent error is the absolute value of the difference divided by the “correct” value times 100.
Is it Possible to have a Percent Error over 100?
Yes, a percent error of over 100% is possible. A percent error of 100% is obtained when the experimental value is twice the true value's value. In experiments, it is always possible to get values that are way greater or lesser than the true value due to human or experimental errors.
How do you Calculate Percent Error and Absolute Error?
The computation of percentage error involves the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error multiplied by 100 to obtain the percentage error.
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