Erro Absoluto
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
E_a = |Δ|
About this calculator
The absolute error calculator determines the difference between the real (or exact) value of a quantity and the approximate value obtained by measurement or calculation. The absolute error is given by the formula E_a = |x_real − x_aprox|, which measures the magnitude of the difference, ignoring the sign. This metric is essential in fields like engineering, physics, and statistics, where data precision is crucial.
To use the tool, simply enter the real value and the approximate value in the indicated fields. The calculation is instantaneous and returns the absolute error. For example, if the real value of an electrical resistance is 100 Ω and the measurement indicated 98 Ω, the absolute error is |100 − 98| = 2 Ω. The smaller the absolute error, the more accurate the approximation.
Absolute error is useful in situations such as instrument calibration, tolerance analysis in mechanical projects, validation of mathematical models, and comparison of numerical methods. However, it does not consider the scale of the value: an error of 1 cm in a distance of 1 m (1%) is different from the same error in 1 km (0.001%). Therefore, in many cases, relative error is more informative.
Cautions: make sure to use the correct real value, as any inaccuracy in that value compromises the calculation. Also, remember that absolute error does not indicate whether the approximation is over or under (only the magnitude). For comparative analyses between different quantities, prefer relative or percentage error.
Frequently asked questions
What does an absolute error of zero mean?
It means the approximate value is exactly equal to the real value, i.e., the approximation is perfect. This rarely occurs in real measurements.
Can absolute error be negative?
No, absolute error is always non-negative because it uses the absolute value of the difference. The sign of the difference (whether the approximation is over or under) is lost.
What is the difference between absolute error and relative error?
Absolute error is the simple difference between values, while relative error is that difference divided by the real value, expressing precision relative to the magnitude of the quantity.
How is absolute error used in practice?
It is used to evaluate measurement accuracy, calibrate instruments, define tolerances in mechanical parts, and verify convergence of numerical methods.
Can I calculate absolute error with negative values?
Yes, the formula works for any real numbers. The absolute value ensures the result is positive, regardless of the sign of the values.