# Relative Error Definition (Science)

What Is Relative Error? Relative error is a measure of the uncertainty of a measurement compared to the entire measurement's magnitude. Caiaimage/Martin Barraud / Getty Images

Relative error is a measure of the uncertainty of measurement compared to the size of the measurement. It's 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:

1. Using an approximation instead of real data (e.g., 22/7 or 3.14 instead of pi or rounding 2/3 to 0.67)
2. 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
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