Absolute Error

TL;DR

• Quantifies how far a measured value is from the true value, ignoring sign.
• Used to assess the precision and accuracy of measurements in scientific and engineering contexts.
• Does not indicate direction of the error; often paired with relative error for more information.

Definition

Absolute error is a measure of the difference between a measured value and the true value of a quantity. It is the magnitude of the difference between the measured and actual values, without considering the direction of the error.

$$\text{Absolute error} = \left| \text{measured value} - \text{true value} \right|$$

Explanation

Absolute error gives the size of the discrepancy between an observed measurement and the true (reference) value. It is concerned only with how large the error is, not whether the measurement is above or below the true value. Smaller absolute error indicates a measurement or calculation is more accurate in magnitude.

Absolute error is commonly used in scientific and engineering fields to evaluate the precision and accuracy of measurements. Because it omits direction, it is often used alongside other measures (for example, relative error) to provide a fuller picture of measurement accuracy.

Examples

Simple measurement example

If a measurement of a person’s height is 5 feet 6 inches, but the actual height is 5 feet 8 inches, the absolute error would be 2 inches.

Instrument calibration

A thermometer may be calibrated by comparing its readings with those of a reference thermometer known to be accurate. The absolute error for the instrument being calibrated is the difference between its readings and the reference thermometer’s readings.

Chemical reaction evaluation

To determine the efficiency of a chemical reaction, amounts of reactants and products measured before and after the reaction are compared. The absolute error is the difference between the measured and expected values of the reactants and products.

Use cases

• Calibration of scientific instruments by comparing measurements to a known standard.
• Evaluating measurement accuracy and precision in scientific and engineering applications.
• Assessing discrepancies in quantities measured before and after experiments (for example, chemical reactions).

Notes or pitfalls

• Absolute error does not provide information about the direction (positive or negative) of the error—only its magnitude.
• Because it omits direction, absolute error is often used in combination with relative error to better understand measurement accuracy.

Related terms

• Relative error