Percent Error Formula

The percent error formula helps us to calculate the exact amount of error that occurred in measuring the dimension or other quantities. The percent error formula is applicable to a wide range of scenarios, one might come across on a daily basis. In this section, we will learn about the percent error formula, and how to use it.

What is Percent Error Formula?

The percent error formula calculates the absolute value of the difference between the measured value and the actual value that is divided by the actual value and multiplied by 100. The percent error formula is about comparing the estimated value with the exact value. In mathematics, the percent error is always represented as a positive number. The Percentage or percent error formula of a given measurement can be expressed using the following expression.

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

Where, '| |" denotes the absolute value sign

Steps to Calculate Percent Error Formula

There are a few steps to be followed while calculating the percent error of a value, they are:

• Step 1: Using the percent error formula, subtract the experimental value from the theoretical value. If the answer is negative, it converts into positive because of the absolute value sign.
• Step 2: Once we have obtained the value, divide it with the actual or theoretical value. We obtain a decimal number.
• Step 3: Convert that decimal number into a percent by multiplying it by 100 and adding the percentage sign - %

Examples Using Percent Error Formula

Example 1: The radius of a nut is measured as 0.5in. The actual value of the radius of the nut was known to be 0.47in. Find the percent error in the measurement.

Solution:  Given,

Theoritical value = 0.47in, Experimental Value = 0.5in 

Using Percent Error Formula,
Percent Error = |(Experimental Value - Theoretical value) / Theoritical value| × 100

Putting the values,
Percent Error = |{(0.5- 0.47) / 0.47}| ×100
Percent Error = |{(0.5- 0.47) / 0.47}| ×100
Percent Error = |0.06| ×100
Percent Error = 6

Therefore, the percent error in the measurement is 6%.

Example 2: The price of a car was estimated to be $12995. The actual price of the car was $13000. Find the percentage error in the estimation using the percent error formula.

Solution:  Given,

Theoritical value = $13000, Experimental Value = $12995 

Using Percent Error Formula,
Percent Error = |(Experimental Value - Theoretical value) / Theoritical value| ×100

Putting the values,
Percent Error = |{(12995 -13000) / 13000}| ×100
Percent Error = |{(-5) /13000}| × 100
Percent Error = |-0.00038461| × 100
Percent Error = 0.03

Therefore, the percent error in the estimation is 0.03%.

Example 3: In a concert, 250 people were estimated to attend but 350 people attended. Using the percent error formula, calculate the percent error in the guess value by the organizers. 

Solution: Given, 

Theoritical value = 350 , Experimental Value = 250

Using Percent Error Formula,
Percent Error = |(Experimental Value - Theoretical value) / Theoritical value| ×100

Putting the values,

Percent error = |(250 - 350) / 350| × 100

Percent error = |-100 / 350| × 100

Percent error = 0.286 × 100

Percent error = 28.6

Therefore, the percent error by the organizers is 28.6%