Absolute Error and Relative Error Calculation Methods

In daily testing work, we often need to use absolute error and relative error. Below, we will specifically learn the detailed calculation methods for absolute error and relative error.

(1) Absolute error: describes the difference between the measured value and the true value:
Absolute error = Measured value − True value

(2) Relative error: compares the magnitude of the absolute error to the true value, usually expressed as a percentage:
Relative error = (Absolute error / True value) × 100%

Note: When the measured value is greater than the true value, both the absolute error and the relative error are positive; when the measured value is less than the true value, both are negative.

Examples
Calculate the absolute error and relative error in the following examples.

(1) COD online reading: 17.7 mg/L, actual water sample value: 20 mg/L. Find the absolute error.
(2) Total nitrogen online reading: 54.6 mg/L, actual water sample value: 50 mg/L. Find the relative error.

Answers
(1) Absolute error = Measured value − True value = 17.7 − 20 = −2.3 (mg/L)
(2) Relative error = (Absolute error / True value) × 100% = (54.6 − 50) / 50 × 100% = 9.2%

A horizontal line drawn above a number indicates that the number is multiplied by 1,000, for example, ⓹ = 5000. (Note: The original text shows a symbol like an overbar; here it is rendered as “⓹” for illustration, meaning 5 with an overbar equals 5000.)