Percent Error Equation Formula Calculator

Assess the percent error of your experimental findings

When you have scientific findings that are intending to get an exact known value, the percent error can be a useful tool for revealing the precision of your calculations. By entering a few details relative to your research, you can quickly obtain the accuracy of your conclusions. This can be useful for students checking their work or for professionals evaluating their proofs.
What is percent error?
Percent error is a method to assess the accuracy of scientific approximations, measurements, and experiments. It can be more technically described as the percent difference between a measured value and the exact known value.
Discrepancies can happen for many reasons, and it is important to understand why the imprecision happened. Using percentage error can help you assess if there was a problem with your estimations, faulty equipment, or a missed step in your experiment, based on the amount of deviation.
Percent error is most commonly used in physics when testing acceleration and velocity, as well as in chemistry when assessing data, density, or chemical reactions. The closer that the percent error is to zero the closer you are to reaching your target.
How to calculate percent error
Percent error is elementary to figure as long as you can say with certainty what the exact known value should be. If the exact value is not known, the standard deviation will help you find the experimental error.
To calculate the percentage error, you should first start by subtracting the true value from the observed value. You may get a positive or negative result, and in most cases, you can take out the negative. However, in chemistry and other sciences, it can be customary to keep the negative value as the outcome can give valuable clues as to the potential issues with the procedure (negative result) or if there are any unintended reactions (positive result).
The next step is to divide the resulting error of the previous calculation, by the exact known value. Doing this may provide a decimal number.
Finally, to convert that figure to a percentage, just multiply by 100 and add a percent sign to the final value.
The formula for the absolute value of percent error can be expressed in the following format:
Percent Error
For any assessments comparing theoretical yields in which keeping the sign is important, just remove the absolute value symbol as in the following example:
Relative equation
Examples
 
Example one
 
The Miami weather forecast called for 10mm of rain but there ended up being 16mm of rain by the end of the day. What was the absolute value of the forecaster’s percent error?
Percent equation calculator
In this case, the weather forecast was off by a percentage error of 37.5%. This is not to be confused with absolute error (more on this later), even though it sounds similar due to the usage of ‘absolute value’.
 
Example two
 
A student establishes the volume of a cubic crystal to be 8.1 cubic cm. What is the student’s percent error if the correct volume of the crystal is 8.4 cubic cm?
Percent equation calculation
equation
percentage
In this instance, the student had calculated a percent error of -0.35%. This means the student’s values came up short and the student should return to verify their initial measurements before repeating the calculations.
Once you work out your answer, you can always check your working by using a percentage calculator.
How to use the calculator
The percent error calculator is very straightforward to use and only requires some data relative to your investigation. For accurate results to be generated it is important to be confident of your exact known values. Let’s review this information together.
Before using the calculator, you should have all the data from your trials on hand.
Step 1:
On the first line of the calculator, observed value, please add the output from your experimental analysis. This is the figure that resulted from your assessment.
Step 2:
On the next line of the calculator, true value, you may add the exact known value that should have been obtained from the test.
Step 3:
View your result in the top right-hand corner of the calculator. The calculator does not have to be reset between calculations, only adjust the information as needed.
With this information, depending on the amount of percent error, you can get an idea of where your procedure went wrong.
Percent error vs. absolute error and relative error?
When it comes to analyzing errors relative to scientific findings, there are many different formats in which to observe the discrepancies.
It is easy to get confused with the term absolute error, which is the difference between the experimental value and an exact known value. It is the first step of the percent error formula where you subtract to obtain the extent of your error.
absolute equation
There is also the relative error, which is the division of the absolute error by the exact known value. This is the second step of the percent error formula, and when you multiply the relative error by 100, you achieve the percent error.
Relative equation
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