Relative error is a very simple concept, it is the difference between a measured value and the actual value expressed as a percent. Relative error is unique as it uses a percent to outline the difference in the values opposed to the actual difference between the two.
A good way to remember what relative error is can be to think of a scale from the doctor's office. When the doctor slowly and precisely is moving the gauge to find the perfect weight that makes the needle at the end sit perfectly and indicate that your weight is exactly that.
Well, the thing is there is the chance the doctor measured wrong or the scale is off a very little amount. That measured value that can be wrong when compared to the actual true value is what is being used when calculating relative error.
Relative error can only requires two variables to be known, the measured value and the actual value. The formula for finding relative error with these values is:
Where:
When you use the relative error tool, you will get a single number as your result which is displayed as a percentage. This percentage is the total difference between the measured value and the actual value. The larger the percentage, the larger the difference between the values and vice versa.
If your result is 10% that means there is a 10% difference, in either direction, between the two values. That is right, since the formula uses absolute values, it takes away any negative values meaning the relative error percent will never be negative.
If you need to find the relative error between two numbers you are in the right place. You can easily do this by following these steps:
You have a food scale at home and like to weight out your food when you are cooking and preparing meals. You are measuring in ounces and pour an entire pack of 16oz pasta onto the scale. For some reason, the scale is reading 14oz, despite the box being 16oz.
Using our relative error tool, you can identify just how far off the measured value, 14, is from the actual value, 16. We plug 14 into the measured value field and 16 in the actual value field and then hit calculate. We got a relative error of 12.5%!
The main difference between these two concepts is that relative error is expressing the difference as a percentage while absolute error is displaying it as the actual value difference. Let's say measured value is 5 and the actual value is 9, the absolute error would simply be 4 but the relative error is 44.44%.
Relative error can never be greater than 1, since 1 is equal to a 100% relative difference. It would be impossible to get more than a 100% difference when calculating this type of problem.
Technically, yes relative error can be negative. It is almost always displayed as a positive percent difference but there may be a one-off situation where a measured value that is less than the actual value would be marked as a negative percent error, but this is highly unlikely. Typically, the negative symbol will be removed to express the percentage as a plain positive percentage.
Create Date: September 30, 2024
Last Modified Date: October 8, 2024
