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Percent Error Calculator


What is Percentage Error?

Many people struggle with the errors in the calculation by not getting the desired results. While calculating, there are chances that the results may vary. Certain factors lead a calculation towards error. Error can be system generated or humanly created.

Percent Error Definition

Error percentage is the difference between approximate values and exact values to the percentage of the exact value. Percentage error formula is used for calculating percent error.

Importance of percent error calculator in daily life

Percent error calculator can be used in many things. Many people think that it is only used in scientific experiments but it's not true.

Percent error can be used in your calculations where you have exact value but the observed value is different such as in return on assets reports or sales tax report where you can also use return on assets calculator and sales tax calculator to calculate your first values respectively.

What is Percentage Error formula?

As per the definition, the percentage error formula is all about comparing approximate value to the exact value. So keeping this fact in front,

we get,

(|Approximate Value- Exact Value| / |Exact Value|) x 100% 

(The “|” symbols mean absolute value, so negative becomes positive)

But before calculating percent error, you need to remember a few things

  • First, find the error
  • you are calculating any value and encountered an error then subtract one value from others and don’t forget to ignore minus sign
  • I estimated 200 People, but 300 came
  • 200-100= -100, as we told you to ignore the minus sign, so the error is 100
  • Then Convert it into the Percentage Error
  • convert your percent error into the percentage error for the percent of the exact value, divide your results by the exact values and make it a percentage
  • Continued 100/300= 0.3%= 30%

But calculating in this way is a direct approach, you should calculate or find percent error or percentage error by using percent error equation which we derived above. The percentage error, in general, is all about comparing either a guess or an estimated value to an exact value to find the percentage or ratio of an error in any calculation.

Can Percent Error be negative?

Percentage error can be either negative or positive. The error will be negative only if the experimental value is less than the accepted value. The error will be positive if the experimental value is larger than the accepted value.

Can we calculate Percent Error without Absolute Value?

Yes, We can calculate percentage error without having absolute value. Absolute value can be skipped, in case to find value in either positive or negative.The formula is

(Approximate Value - Exact Value / Exact Value) x 100%

How to find Percent Error?

To find error, the formula for percentage error is

(|Approximate Value - Exact Value| / |Exact Value|) x 100% or

Percent Error = (|(Observed Value − Accepted Value) / Accepted Value|) × 100


Percentage Error = (|E-T| / |T|) X 100


E = Experimental Value

T = Theoretical Value

Where “|” indicates the absolute value to convert a negative value into the positive one.

Calculations by using Percent Error equation

Imagine 70 people would turn up to the concert, but 80 did. We have to find the percentage error using the percent error formula.

We'll find the approximate value alongside exact value in a given case. In the example which is 70 and 80 respectively.

Approximate Value: The value is based on informed knowledge and closest to the exact value.

From here you can also understand that percent error can be used in our daily life problem. Same as you can also use margin calculator to know the differences between the given values.

Exact Value: The Value which cannot be estimated, it must be precised. In some cases, the actual value to which an approximate value is going to be compared is also called exact value.

Now if we put approximate value and exact value in the given formula for percent error

|70-80| / |80| x 100% = 12.5%

So you were in error by 12.5%

Example 2: You need to evaluate that a car park held 240 cars, but it only counted 200 parking spaces available. Find the percent error using the percent error formula.

(|240-200| / |200|) x 100% = 20%

The parking space had a 20% error.

How to calculate Percent Error step by step?

To calculate percent difference or percentage error, you need to follow these steps

  • First of calculating the error by subtracting one value from others and ignore any minus sign
  • We get decimal number by dividing the error by the exact value
  • Convert the results into a percentage by multiplying by 100 and adding a “100%” sign

What are Theoretical Value and Observed Value in Percent Error Formula?

Well, you will find on many places theoretical values and observed values for the exact values and approximate values, respectively. The concept of theoretical and observed values is the same, but it is mostly used to calculate the percent error for physics formulas. Here you can also use our free theoretical yield calculator if you are doing science work.

How to use Percent Error Calculator?

Using our percentage error calculator is very simple. You only need to put true value and observed values (The name of values can be varied, but the actual meaning remains the same) and then click on the results.

You will get your results within a few seconds without any errors or omissions. Our tool is free of cost usage with efficient and swift results.

We hope you liked our article !! Calculatored provides tons of free tools such as integral calculator and derivative calculator.

Please provide your valuable feedback below. Best of luck with your learning.

Shaun Murphy

Last updated: September 09, 2020

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.

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