Percentage Error – Formula, Definition, and Computation!

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When we measure anything throughout an analytical process, the percentage of mistakes shows how large our errors are. Fewer mistakes in percentage terms suggest that we are getting close to the acceptable or original value. For instance, a 1% mistake indicates that we were so near to the allowed number, while a 48% error shows that we were fairly far from the genuine value. Measurement inaccuracies are frequently unavoidable for a variety of reasons, including the possibility of handshaking, the possibility of inaccurate materials, or the potential for estimation errors on the part of our tools. The Percentage Error calculation will show us how much these inescapable mistakes affected our results.

What is meant by Percentage Error?

Do you know that the other name for percentage error is the percent error? Every time we do an experiment, the findings either match the real value or, occasionally, deviate from it. The discrepancy between the actual value and the estimated value is known as an error.

The cause of mistakes is basically either unavoidable flaws in the measuring device or the limits of human sight. Errors can range in magnitude, therefore, we occasionally need to determine if the measurement's inaccuracy is too large to be useful.  If we find that the mistake is minimal, then we are more likely to be closed around the true value. So, researchers reached up with a path to choose how much guess is off.

What is the Percent Error Formula?

Wondering why there is a need for a formula for doing percent error? So it helps you to do calculations after.  The percent error formula indicates the absolute value, which is found after measuring the difference between the measured value and the actual value, along with dividing by the actual value and multiplying by 100.

It shows the difference that occurred once you compare an estimated value with the exact value. In mathematics, it is generally expressed as a positive number.  It can be defined using the following expression.

Percent Error = |(Experimental Value - Theoretical value) / Theoretical value| × 100

Where '| |" denotes the absolute value sign.

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How to Calculate Percentage Error?

Want to learn the basic steps so that you can easily calculate percentage error? To determine the proportion of error in any observation or experiment, follow the methods outlined below:

Step 1:

Subtract one of your values from the other to calculate the error's value. If you are retaining the sign in your equation, the sequence of the subtraction is irrelevant. If your equation, however, has a minus sign, you must subtract the actual value from the experiment's observed value in order to determine your error.

Step 2:

Next, divide the difference between the two values (also known as the error value; be careful not to mix it with your experimental or measured value). You will have a decimal after the division.

Step 3:

The final step is to convert the decimal number you obtained in the previous step into a percentage value by multiplying it by 100.

Step 4:

The percent symbol (%) must be added to determine your percentage mistake.

Now you have learned how to calculate percentage error. It is a moment for you to comprehend why to estimate percentage error. So, read the listed information, which help you to understand why it is important for you to estimate percent error.

Why Estimate Percent Error?

Percentage errors are used to determine whether your measurements are accurate.  It is a useful metric to find out whether you are nearer to the actual value that you have estimated. Use it to measure how near an estimate is to the actual value, in general. When an approximation value is near the true value, there are fewer mistakes. The % inaccuracy rises as the estimations go farther from the true value.

These inaccuracies may be brought on by the measuring device, the estimating procedure, the staff, or a combination of factors. Your estimations may be deemed invalid if the mistake grows to a significant enough size. You'll then need to make the necessary corrections. However, because it differs per topic area, there is no universal cutoff point.

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The intent for computing the percentage error relies on the context.  Analysts are using it to compare estimated values to general values to evaluate the facts of their measurements in scientific studies and quality management projects. Alternatively, researchers utilize it to approximate a value from experimentation to a hypothetical or true value to comprehend the facts of their experimental analyses.

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How to find Percentage Error?

Percentage error can be calculated using three simple steps:

• Computation of the error

Absolute Error = Approximate Value – Exact Value (actual value)

In the above-listed expression, we just subtract the approximate value from the exact value to get an absolute error.

• Divide the error by the actual value

Relative Error = |Approximate Value – Exact Value|/Exact Value

 Now, once you get the absolute value, it is time to divide the error by the actual value to get a relative error

• Convert that to a percentage

Percent Error = |Approximate Value – Exact Value|/Exact Value × 100%

Now you can convert the relative error into a percentage error by multiplying by 100 and attaching the "%" sign.

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