# How do you calculate relative error?

To calculate relative error, you must first calculate absolute error. Absolute error is the quantitative amount of incorrectness between an estimate and the actual value of a measurement, while relative error is a comparison between the absolute error and the total size of the measured item.

To calculate absolute error, subtract the experimental value, or estimate, from the actual value, and discard the negative sign, if applicable. To calculate relative error, divide the new number, the absolute error, by the real value. Because relative error is most often designated as a percentage, multiply this quotient by 100 to complete the calculation.

For example, to calculate the relative error of the distance from one tree to another, a person could pace off the steps in between the two trees and guess that the distance is 22 feet. If the actual distance between the trees is determined to be 21 feet 9 inches, the absolute error is 3 inches, or 0.25 feet. To calculate the relative error, divide 0.25 feet by the actual value, 22 feet, to get 0.01136. Multiply that number by 100 to determine the relative error, in percentage form, is 1.14 percent. This is a very low relative error.

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