October 4, 2025

What Is Absolute Error

Q: What is the difference between absolute error and relative error?

Absolute error is the raw numerical difference between measured and true values, whereas relative error expresses this difference as a proportion or percentage of the true value, offering insight into its significance.

Q: Can absolute error be negative?

No, absolute error is always non-negative because it is calculated using the absolute value function, which disregards the direction of the deviation.

Q: Does a smaller absolute error always indicate a better measurement?

Generally, a smaller absolute error means a measurement is closer to the true value, implying higher accuracy. However, 'better' can also depend on the context and the magnitude of the quantity being measured.

Q: Is absolute error related to precision or accuracy?

Absolute error is a direct measure of accuracy, as it quantifies how close a single measurement is to the true value. Precision, in contrast, refers to the consistency or reproducibility of multiple measurements.

Learn about absolute error, a fundamental measure of the difference between a measured value and the true value, without regard to direction.

Have More Questions →

Definition of Absolute Error

Absolute error is the magnitude of the difference between a measured value (or observed value) and the true value (or accepted value) of a quantity. It quantifies the raw discrepancy without indicating whether the measurement was too high or too low.

How to Calculate Absolute Error

The formula for absolute error is straightforward: Absolute Error = |Measured Value - True Value|. The absolute value ensures that the error is always non-negative, representing only the size of the deviation from the actual value.

Practical Example

If the true length of a desk is 100 cm, and a student measures it as 98 cm, the absolute error is |98 cm - 100 cm| = |-2 cm| = 2 cm. If another student measures it as 103 cm, the absolute error is |103 cm - 100 cm| = |3 cm| = 3 cm.

Importance in Science and Engineering

Absolute error helps in understanding the accuracy of measurements, indicating how close an observed value is to the true value. While it provides the extent of the error, it doesn't convey its significance relative to the size of the quantity being measured, which is where relative error provides additional context.

Frequently Asked Questions

What is the difference between absolute error and relative error?

Can absolute error be negative?

Does a smaller absolute error always indicate a better measurement?

Is absolute error related to precision or accuracy?