Table of Contents
What Is Relative Error?
Relative error is a measure of how inaccurate a measurement is, expressed as a fraction (or percentage) of the true value. Unlike absolute error, which only tells you the magnitude of the deviation, relative error puts the error in context by comparing it to the size of the quantity being measured.
For example, an absolute error of 1 cm is significant when measuring a 10 cm object (10% relative error) but negligible when measuring a 100 m building (0.001% relative error). This makes relative error essential for comparing the accuracy of measurements across different scales.
Formula
Relative Error = |Measured - True| / |True|
Percent Error = Relative Error × 100%
The relative error is dimensionless (a pure number), while the absolute error has the same units as the measurement. Percent error is simply the relative error expressed as a percentage for easier interpretation.
Types of Error Comparison
| Error Type | Formula | When to Use |
|---|---|---|
| Absolute Error | |Measured - True| | When units matter and scale is constant |
| Relative Error | |Measured - True| / |True| | Comparing accuracy across different scales |
| Percent Error | Relative Error × 100% | Reporting accuracy to a general audience |
| Relative Accuracy | 1 - Relative Error | When you want to express closeness, not deviation |
Frequently Asked Questions
What is a good relative error?
This depends on the field. In chemistry, less than 5% is often acceptable. In precision engineering, relative errors below 0.1% may be required. In social sciences, errors up to 10% can be tolerable. Always compare against the standards of your specific discipline.
What if the true value is zero?
Relative error is undefined when the true value is zero, because you would be dividing by zero. In such cases, use absolute error or consider alternative metrics like the mean absolute error (MAE) or a symmetric relative error formula.