Absolute error refers to the difference between a measured value and the true value, whereas relative error is defined as the absolute error divided by the true value.

Absolute error quantifies the deviation of a measurement from the true value. It can be calculated using the formula:

For instance, if a student measures the length of a table to be $1.5$ meters, but the actual length is $1.6$ meters, the absolute error would be:

In contrast, relative error provides context by considering the size of the true value. It is calculated as follows:

Using the previous example, with a true length of $1.6$ meters, the relative error would be:

Relative error is particularly useful for comparing the accuracy of measurements with different magnitudes. For instance, if two students measure the length of the same table using rulers of varying scales, their absolute errors may differ. However, their relative errors will provide a more comparable assessment of measurement accuracy.

In summary, absolute error measures the extent of deviation from the true value, while relative error expresses how significant that error is in relation to the true value.