Percent Error Formula

Formula to Calculate Percent Error

Percentage error formula is calculated as the difference between the estimated number and the actual number in comparison to the actual number and is expressed as a percentage, to put it in other words, it is simply the difference between what is the real number and the assumed number in a percentage format.

In Science-related matters, the concept of percentage error formula is often used wherein the variance between the experimental value and the exact value is to be determined. This calculation will help us in comparing a value that is derived from the experiment with exact or true value. The percentage error also provides information as to how close one is in their measurement or their estimation to the true or the real value.

PE = |Experimental Value – Exact Value| / |Exact Value| * 100
Percent Error Formula

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Source: Percent Error Formula (wallstreetmojo.com)

Steps to Calculate Percent Error

To calculate the percent error, one can follow the below steps:

  1. The first one needs to obtain the experiment (assumed) value and the exact value.

  2. Find the variance between them and then take the absolute value; that is, one needs to ignore any negative sign, if any. This is known as the error.

  3. Next, find out the absolute value of exact or true value.

  4. Divide the absolute error (non-negative), which was determined in step 2, by absolute true value or the exact value.

  5. Now, finally multiply the result that is obtained in step 4 by 100 so that the result is converted into percent value and then add a “%” symbol to the result.

Examples

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

Example #1

A new tourist place statue of unity was established recently in Gujarat in India, and it was estimated that around 3,00,000 people would turn around on its inauguration day. But the exact number of people that came for its inauguration was around 2,88,000. You are required to calculate the percentage error.
Below is given data for calculation of Percent Error
Percent Error Example 1

Therefore, calculation of the Percent Error will be as follows,

Percent Error Example 1.1

=(300000-288000)/288000*100

Percent Error will be –

Percent Error Example 1.2

Percentage Error= 4.17%

Example #2

Avenue Supermarket, a retail company, operating under the name “Dmart,” is an expansion phase, and the company plans to open new branches in new cities. At the start of the financial year, the company planned and estimated to open 24 branches, however by the end of the year; the company opened only 21 stores. The company has approached you to calculate the percentage error that they made during initial planning.

Below is given data for calculation of Percent Error

Percent Error industry Example 2

Therefore, calculation of the Percent Error will be as follows,

Percent Error industry Example 2.1

=(24-21)/21*100

Percent Error will be –

Percent Error industry Example 2.2

Percentage Error= 14.29%

Example #3

As per a poll that was conducted by a news channel during an election campaign where they estimated for XYZ party to win 278 seats out of 350 seats. After the results came out, it turned out that the XYZ party managed to win 299 seats out of 350 seats. The News channel is perplexed by the actual outcome and now wants to know what margin error they made and how much they lagged. Calculate the percentage error.

Below is given data for calculation of Percent Error.

Example 3

Therefore, calculation of the Percent Error will be as follows,

Example 3.1

Percent Error will be –

Example 3.2

Percentage Error=-7.02%

NOTE: Even though in this example, the output came in negative but with symbols “|” which stands for absolute value, and hence the number +21 is derived.

Uses of Percent Error Formula

The percent error appears to be a simple calculation, but it is very useful as it provides us with a number that will depict our error. Further, it is used whenever it is crucial to know the amount of error which is present in the data, and it is necessary to know the reason for the error, whether the reason is due to by equipment impairment or by one’s own error or mistake in the assumptions or estimations.

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