What is Percent or Percentage Error?
Many people struggle with the errors in the calculation by not getting the desired results. Once you start measuring the data of a particular thing for a specific purpose, there are chances that the resulting number can be varied from the actual value. Now, certain things can lead to an error but mostly human error. That is where you can use the percent error formula to measure the difference between approximate values and exact values to the percentage of the exact value.
Derivation of Percent Error Formula
As per the definition, the percent 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 the 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 Formula 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.
How to use Percent Error Formula or How to Calculate Percent Error?
As we derived earlier, 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
Here, E= Experimental Value
T= Theoretical Value
Where “|” indicates the absolute value to convert a negative value into the positive one.
To calculate percent difference or percent 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
Examples of Percent Error Calculation Using Percent Error Formula
Example 1: Imagine 70 people would turn up to the concert, but 80 did. Find the percent error using the percent error formula.
To find the percent error, find the approximate value alongside exact value in a given case. In the example which is 70 and 80 respectively. Now here a question rose. What exactly is an approximate value and the exact values. So let’s make it clear your perception about approximate and exact values to make it better understand the usage of percent error formula.
Approximate Value: The value is based on informed knowledge and closest to the exact value.
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.
We are hopeful now you are clear about the exact and approximate values so let’s continue the example.
Example 1 Continued: Now put approximate and exact values in the given percent error formula
|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.
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.
Can We Calculate Percent Error without “Absolute Value?”
Yes, we can also use the formula without calculating the absolute value. If you want to get a result in either positive or negative which may be useful to know, then you can skip the absolute value. The formula would look like this without absolute value
Approximate Value- Exact Value / Exact Value x 100%
Why Use Percent Error Calculator?
Most of the time, errors can be experienced given multiple reasons which are often associated with human error. This can also happen while finding or calculating the percent error or percent difference for various reasons. So what should one do to avoid human side mistakes? The answer is very simple and straightforward. Use a computer-generated error-free percent error calculator. Where human side limits you while performing calculations, a percent error calculator can make the computation process easy without considering any limitations. When it comes to the best online available percent error calculator, percent error calculator outshines every other online error finding calculator.
How to Use a Percent Error Calculator?
Using our percent error calculator is as simple as using our any other online calculator. You only need to put accepted 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. Are you looking for the best online percent error calculator? Try Percent Error Calculator without wasting any further time to get your desired results.