Erro Relativo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
E_r = |Δ|/|real|
About this calculator
The relative error calculator determines the precision of a measurement or approximation relative to the true value. The relative error is defined as the absolute error divided by the absolute true value, i.e., E_r = |Δ| / |real|. It expresses the magnitude of the error as a fraction or percentage, allowing comparison of accuracy across different scales.
To use the calculator, enter the true (or exact) value and the approximate (or measured) value. The tool automatically computes the absolute error and then the relative error. The result can be displayed as a decimal or percentage. It is useful in scientific experiments, engineering, numerical analysis, and any situation where result accuracy is evaluated.
Relative error is preferred over absolute error when comparing measurements of different magnitudes because it normalizes the error by the true value. For example, an error of 1 cm in a distance of 100 m (0.01%) is much smaller than the same error in 1 m (1%). Caution: if the true value is zero, relative error is undefined; in that case, use absolute error.
Common applications include instrument calibration, validation of mathematical models, quality control, and tolerance adjustment. Remember that relative error does not indicate the direction of the error (overestimation or underestimation), only its magnitude. For a complete analysis, combine it with absolute error and the error sign.
Frequently asked questions
What does a relative error of 0.05 mean?
It means the absolute error is 5% of the true value. For example, if the true value is 100, the absolute error is 5.
Can I use relative error if the true value is zero?
No, relative error is undefined when the true value is zero because it involves division by zero. In that case, use absolute error.
What is the difference between relative error and percent error?
Percent error is relative error multiplied by 100%. Both measure the same quantity, just on different scales.
Can relative error be negative?
Relative error is always non-negative because it uses the absolute value of the absolute error. To know whether the approximate value is larger or smaller than the true value, check the sign of the absolute error.
How to interpret a very small relative error?
A small relative error indicates high accuracy: the approximate value is very close to the true value. For example, 0.001 means 0.1% error.