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The result is the relative error. Note that in most cases the unit of measurement of the absolute error will be the same as the unit of measurement of the actual value, and the units will cancel each other. This leaves the relative error without any units of measurement. This simple equation tells you how far off you were in comparison to the overall measurement. A low relative error is, of course, desirable. To continue the example of measuring between two trees: Your Absolute Error was 2 feet, and the Actual Value was 20 feet. 2ft20ft{\displaystyle {
rac {2ft}{20ft}}} Relative Error =.1{\displaystyle =.1} Leave the relative error in fraction form, complete the division to render it in decimal form, or multiply the resulting decimal form by 100 to render your answer as a percentage. This tells you what percentage of the final measurement you messed up by. If you are measuring a 200 foot boat, and miss the measurement by 2 feet, your percentage error will be much lower than missing the 20 foot tree measurement by 2 feet. The error is a smaller percentage of the total measurement. 2ft20ft=.1{\displaystyle {
rac {2ft}{20ft}}=.1} .1100=10%{\displaystyle .1*100=10\%} Relative Error. Once you understand the difference between Absolute and Relative Error, there is really no reason to do everything all by itself. Simply substitute the equation for Absolute Error in for the actual number. Note that the vertical bars are absolute value signs, meaning anything within them must be positive. Relative Error =|MeasuredActual|Actual{\displaystyle ={
rac {|\mathrm {Measured} -\mathrm {Actual} |}{\mathrm {Actual} }}} Multiply the whole thing by 100 to get Relative Error Percentage all at once. Let the audience know the units you're using for measurement. However, the relative error does not employ units of measurement. It is expressed as a fraction or a percentage, such as a relative error of 10%.
Divide the Absolute Error by the Actual Value of the item in question to get Relative Error. Multiply the answer by 100 to get an easier to understand percentage. Calculate Relative Error all at once by turning the numerator (top of fraction) into your Absolute Error equation. Always provide units as context.