Relative Error Definition (Science)

Relative Error Definition (Science) Relative error is a measure of the uncertainty of measurement compared to the size of the measurement. Its used to put error into perspective. For example, an error of 1 cm would be a lot if the total length is 15 cm, but insignificant if the length was 5 km. Relative error is also known as relative uncertainty or approximation error. Reasons for Relative Error Relative error compares a measurement to an exact value. The two reasons for this error are: Using an approximation instead of real data (e.g., 22/7 or 3.14 instead of pi or rounding 2/3 to 0.67)Imprecise measurement due to instrumentation (e.g., a ruler measuring to the nearest millimeter) Relative Error Versus Absolute Error Absolute error is another measure of uncertainty. The formulas for absolute and relative error are: EA | V - Vapprox | ER | 1 - (Vapprox / V) | Percent error is then: EP | (V - Vapprox) / V | x 100% Relative Error Example Three weights are measured at 5.05 g, 5.00 g, and 4.95 g. The absolute error is  ± 0.05 g.The relative error is 0.05 g/5.00 g 0.01 or 1%. Sources Golub, Gene; Charles F. Van Loan (1996). Matrix Computations – Third Edition. Baltimore: The Johns Hopkins University Press. p. 53. ISBN 0-8018-5413-X.Helfrick, Albert D. (2005) Modern Electronic Instrumentation and Measurement Techniques. p. 16. ISBN 81-297-0731-4