**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:

- 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:

E_{A} = | V - V_{approx} |

E_{R} = | 1 - (V_{approx} / V) |

Percent error is then:

E_{P} = | (V - V_{approx}) / 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