What is Percentage Error? Percentage error is the measurement of a discrepancy between the observed and the accepted or true value. When you measure data, the result will often be different from the true value. This error could creep in because of many reasons like human error and because of limitations of the devices that have been used in the measurement. This is where it becomes essential to calculate the percentage error.

To calculate the percentage error, you need to involve the absolute error, the difference between the observed and true values. The absolute error is then divided with the true value, and this results in a relative error. The answer needs to be multiplied by 100 to get the percentage error.

Percentage Errors In Experiments

When you experiment, then you may get results that will match the actual value. They, however, could sometimes even vary from the actual value.

Error is the difference between the estimated and the actual value. The measurement errors could occur because of various faults in the measuring instrument and the elimination in the human eye.

Errors can come in various forms and, at times, may also make the measurement useless. If the error is small, then it states that we are close to the actual value.

Key Points Of Percentage Error

The main reason why you need the percentage error is to gauge how close the measured and the true value are. It is the difference between the experimental and the theoretical value, divided by the theoretical value and then multiplied by 100 to get the percent value.

Percent error is usually expressed as a positive number. There are chances when it could be a negative value as well. The sign determines if the recorded value is above or below the expected value. Percent error is a type of error calculation. The others are absolute and relative error calculations.

Percent Error Formula

Let us now understand what the percentage error formula is and to what extent these errors affect the experiment results.

Percentage error = (Actual value – estimate value)/estimated value *100

In most cases, the percentage error is expressed in the form of a positive value. Absolute value can, at times, be termed as a theoretical or true value. The absolute value of the error is divided with a true value, and this is then shown with a percentage.

Calculation Steps For Percentage Error

To calculate the percentage error, here are the steps to be followed:

• Subtract one value from the other. If you are not using the sign, then the order does not matter. If you are going to keep the signs, then subtract the theoretical value from the experimental value. This is the error in your calculation.
• Now divide the error with the ideal or the exact value. This will give you a decimal number. You should not use the measured or the experimental value.
• Convert the decimal into a percentage by multiplying it with 100.
• Add a percent symbol to report the value of percent error.

Can You Have A Negative Percentage Error?

Usually, the percentage error is calculated as positive because it is the error amount involved, and thus the sign is not important. However, in some studies, say in chemistry, you need the sign of the error. In such cases, you will not take the absolute difference between the two values.
Here you also need to be careful on the subtraction order where you will have to subtract the measured and the true value. So if the percentage error is negative, then the measured value will be higher than the accepted or true value. However, unless it is specified, you should always calculate the absolute value and then report the percentage error as a positive number.

You need to know the accurate or true value of the boards’ length and determine the percentage error in each measurement. Like for example, imagine that you estimated the board length and measured it as 22 cm. A friend measured the same board and calculated it as 18cm. You check the manufacturers’ document and find that the length of the board is 20cm. This is the estimated accepted value.
Below we calculate the percentage error estimates for the two measurements taken above. Both had an error of 1%. The friend made an error on the lower side, and thus it is negative. You have made an error on the higher side, and thus it is positive.

Is There Anything As A Good Percent Error?

What is a good amount of error depends on the case under consideration? Suppose you have to calculate the distance between Delhi and Noida, and your estimate was 25 km, and the exact distance is 30km. This will not make much of a difference.
However, if the same distance was used to send a satellite signal, this could cause the whole mission to get into trouble.

Solved Examples

The radius of a circular sheet is 15 cm long, but the package label states 17cm. What is the measured percentage error?

The measured value is 15cm, and the accepted value is 17cm. Subtract the measured and the accepted value. The answer is 2cm. The absolute value is 2cm. Divide this by the accepted value.

So you calculate 2cm/17cm = 0.12. Multiply this answer by 100, and you get 12%.

Thus the percentage error of this measurement is 12%.

Emily weighs an object on balance and gets a recorded weight of 13.62grams. Her mother told her that something was wrong and that the balance gave a 22.22% higher reading. What is the object’s actual mass?

The measured value is 13.62 grams, and the percentage error is 22.22%.

Percentage error = (Measured value – true value)/true value*100

Putting the values in this equation gives us the following:

22.22 = (M-TT)/TT*100

Substituting the value in the equation, we get the answer as 11.143 gms.

Conclusion

Percentage error is thus the difference between the actual and the estimated value compared to the actual value. It is expressed in the format of a percentage. You thus find the difference between the actual and the estimated answer, divide it by the actual answer and express the figure obtained as a percentage. Percentage errors are thus used to measure how huge the error is when something is measured.