Percent Error Formula

Percent Error Formula

The term “per cent error” refers to the percentage-based difference between an item’s exact or known value and its approximate or measured value. It is used to report the discrepancy between the experimental value and its true or exact value in scientific experiments. As a percentage of the precise value, it is calculated. As an illustration from the real world, if the number of gum balls in a gum ball machine is estimated and then actually calculate the number of gum balls, the percentage error can be determined. When estimating the value of something, the per cent error shows how far off the resulting numbers are from the actual value. 

The Percent Error Formula (Approximate or Experimental Value – Exact or Known Value/Exact or Known Value) / 100. The approximation is very close to the actual or true value if the per cent error is close to 0. The accuracy of the calculations can be determined using this Percent Error Formula. The per cent error is typically expressed as a positive number for most applications. But in some sciences, like Chemistry, it is usual to express it as a negative number because a positive value in Chemistry would indicate a potential issue with the experiment or unaccounted-for reactions.

To determine the per cent error in any experiment or observation, the steps listed below must be taken: The “error” value is obtained by deducting one value from another. The order is irrelevant if the sign is not written, but if a negative sign is mentioned, then there is a need to subtract the exact value from the measured value to obtain the “error” value. 

Percentage Error Formula

The difference between the estimated and actual values in relation to actual values—expressed as a percentage—represents the percentage error. To put it another way, divide the difference between the true answer and the guessed answer by the true answer to get the percentage.

When measuring something during the analysis process, the percentage of errors tells how significant the errors are. Close to an acceptable or actual value is indicated by a small percentage error. For various reasons, such as shaking hands, accurate equipment, or the lack of direct measurement capabilities in our tools, measurement errors are frequently avoided. Numerous factors, most commonly human error, can lead to the error. However, it might also be because of the constraints imposed by the tools in use. Calculating the percentage error is crucial in these circumstances.

How to Calculate Percent?

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

1. By utilising the unitary approach.
2. By changing the fraction’s denominator to 100.

It should be noted that when the denominator is not a factor of 100, the second method of percentage calculation is not applied. In these situations, the unitary method is employed.

Method for Finding Per Cent Error

To calculate the per cent error, students need to know the estimated value and the original value. They must first calculate the difference between the original value and the estimated value. The value might be either positive or negative. The warning sign can be ignored by students. The estimated value must be subtracted from the original value. Students will divide the difference by the original value after determining the difference, then multiply by 100 to obtain the per cent value. Finding the per cent error for any experiment is done in this manner. 

Solved Examples for Percent Error

It is important to solve questions that are based on Percent Error Formula. All the questions can be easily solved by applying the Percent Error Formula. Students that are unable to solve questions regularly are advised to take help from Extramarks. 

The Benefits of Finding Per Cent Errors

The calculated value and the theoretical value of the known value make up the test’s value. The percentage that is closest to zero indicates that the resulting value is very close to reaching the desired result, which is positive.

When something is rated on a test, the percentage of errors is important for knowing how serious the errors are. Low values indicate that it is close to being acceptable or actual. For instance, a 1% error indicates that output is closer to the excellent value and 37% points closer to the immediate value than the actual value. The process of identifying percentage errors has many advantages. Here are a few benefits of locating percentage errors:

Accuracy depends on percentage error. The accuracy of a value is its resemblance to its initial value. The error percentage is calculated by multiplying by 100 and dividing the discrepancy between the approximate and actual values. Knowing how close the resultant value is to the actual value is the key advantage of finding a percentage error. The error rate could be as high as the amount of awareness or as low as carelessness. In other words, if the percentage error is low enough, it can be ignored, but if it is high enough, students need to calculate or quantify things in order to get the total value.

Few Worked Examples:

Students will learn proper implementation of the Percent Error Formula if they practice questions regularly. It is crucial to keep practising questions relating to each chapter. The Percent Error Formula needs to be revised periodically. Revision of the Percent Error Formula helps in solving questions effectively. By practising questions regularly, students will be able to remember the Percent Error Formula for a longer period of time.