Updated July 27, 2023
Percent Error Formula (Table of Contents)
- Percent Error Formula
- Examples of Percent Error Formula (With Excel Template)
- Percent Error Formula Calculator
Percent Error Formula
The percent error formula is commonly used in scientific reports, particularly in chemistry. It aims to determine the disparity between a measured or experimental value and an accepted or true value.
By calculating the percent error, one can assess how much the measured value deviates from the exact value. The computation involves the absolute error, typically represented as a positive value, although, in chemistry and other sciences, it is customary to retain a negative value when necessary. The positive or negative nature of the error holds significance. A percent error close to zero or equal to zero indicates that the user’s approximation is very close to the target value, which is encouraging. However, the user must understand the underlying cause and rationale behind the error, which could stem from experimental inaccuracies or mistakes in estimation. The formula compares an estimation or guess and an accurate value.
The formula for Percent Error –
Examples of Percent Error Formula (With Excel Template)
Let’s take an example to understand the calculation of Percent Error in a better manner.
Example #1
The density of the aluminum block is 2.68 g/cm cube, while the density of the same aluminum block at room temperature is 2.70 g/cm cube. Next, calculate the Percent Error of the measurement.
Solution:
The formula to calculate Percent Error is as below:
Percent Error = |(Experimental Value – Theoretical Value)| / |Theoretical Value| * 100
- Percent Error = |(2.7 – 2.68)|/ |2.68| * 100
- Percent Error = 0.75%
Example #2
The user needs to find the volume and mass of a paper cube in the experimental lab. When the user calculates the measurements’ value, it gets the value as 8.78 g/cm cube. At the same time, the cube’s accepted density is 8.96 g/cm cube. Calculate the percent error.
Solution:
Percent Error = |(Experimental Value – Theoretical Value)| / |Theoretical Value| * 100
- Percent Error = |(8.96 – 8.78)| / |8.78| * 100
- Percent Error = 2.05%
Example #3
A scale wrongly measures a value of 10 cm due to some marginal error in the computation. The user needs to calculate the percent error of the measurement when the scale’s actual value is 12 cm.
Solution:
Percent Error = |(Experimental Value – Theoretical Value)| / |Theoretical Value| * 100
- Percent Error = |(12 – 10)| / |10| * 100
- Percent Error = 20%
Explanation
The steps to calculate the formula is:-
- Subtract one value from another as the sign of the formula is not a matter, so any value can be subtracted from any value. The resultant value is your error value which is simply calculated by subtracting one value from another.
- Divide the error value, computed by the exact or theoretical value, which will then result in a decimal number.
- After computing, the decimal value simply converts eh decimal number computed into a percentage by multiplying it by 100.
The formula will show a value in percentage form.
Relevance and Uses
- The keys to correctly reporting percent error are knowing whether or not to drop the sign (positive or negative) on the calculation and reporting the value using the correct number of significant figures.
- It is frequently used in the analysis of scientific research by physicians and in chemistry. When used to do experiments in labs, students also use the percent error formula to determine the variance. The acceptable range of error depends on a case-to-case basis, and the quantum of percent error must always be determined beforehand when experimenting with a particular test in the lab. Using value with a high percent error in measurement is the judgment of the use.
Percent Error Formula Calculator
You can use the following Calculator
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| Theoretical Value | |
| Percent Error | |
| Percent Error = |
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Recommended Articles
This has been a guide to Percent Error Formula. Here we discuss how to calculate Percent Error along with practical examples. We also provide a Percent Error calculator with a downloadable Excel template. You may also look at the following articles to learn more –
