Percent Error Formula

Percent Error Formula (Table of Contents)

Percent Error Formula
Examples of Percent Error Formula (With Excel Template)
Percent Error Formula Calculator

Percentage error formula is being used in many scientific reports and especially chemistry, the formula is used to measure the difference between a measured or experimental value and a true or an exact value. The purpose of the percent error formula is to gauge how different is the measured value is from the exact value. The computation of the percent error formula involves the absolute error which simply is most of the times is denoted in a positive value. Note for chemistry and other sciences, it is customary to keep a negative value. Whether error is positive or negative is important. A percentage error formula which is close to zero or equal to zero signifies that the user is very close to the targeted value which is a positive sign for the user. But, it is very important for the user to know the reason and the rationale behind the cause of the error which can occur due to various of reasons such as an error occurred during the experiment or mistake in its own estimation. The formula is all about comparing a guess or an estimate to an exact value.

The formula for Percent Error –

Percent Error = |(Experimental Value – Theoretical Value)| / |Theoretical Value| * 100

Examples of Percent Error Formula (With Excel Template)

Let’s take an example to understand the calculation of Percent Error in a better manner.

You can download this Percent Error Template here – Percent Error Template

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 to be 2.70 g/cm cube. Calculate the Percent Error of the measurement.

Solution:

Percent Error is calculated using the formula given 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 the mass of the cube of a paper in the experimental lab. When the user is calculating the value of the measurements it gets the value as 8.78 g/cm cube. Whereas, the accepted density of the cube is to be 8.96 g/cm cube. Calculate the percent error.

Solution:

Percent Error is calculated using the formula given below

Percent Error = |(Experimental Value – Theoretical Value)| / |Theoretical Value| * 100

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Percent Error = |(8.96 – 8.78)| / |8.78| * 100
Percent Error = 2.05%

Example #3

A scale measures wrongly 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 actual value of the scale is to be 12 cm.

Solution:

Percent Error is calculated using the formula given below

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 value 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 value.
Divide the error value which is computed by the exact value or the 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 of Percent Error Formula

The keys to reporting percent error correctly are to know whether or not to drop the sign (positive or negative) on the calculation and to report the value using the correct number of significant figures.
It is frequently used in the analysis of scientific research and is used by the physician and in the field of chemistry. Students also when use to do experiments in labs use the percent error formula in order to determine the variance. The acceptable range of error depends on the case to case basis and the quantum of percent error needs to be determined beforehand when experimenting a particular test in the lab always. The use of value with a high percent error in measurement is the judgment of the use.