# Absolute Error of Measurement

Absolute error of a measurement is the difference between the measured value of an object and its true value.

When we take the measurement of an object, it is possible that the measured value is either a little more or a little lower than its true value, that is, an absolute error has occurred.

For example, if a scale (a measurement device) states the weight 10KG but you know the true weight is about 9KG, then the scale has an absolute error of 1KG ($ 10KG-9KG=1KG$).

This error may be caused by the scale used itself not measuring the exact amount of measurement you are trying to measure. For example, your measuring device may be accurate to the nearest KG. That is, if the weight is 9.6KG, your scale may “round up” and gave 10KG. Thus, the absolute error is about $ 10KG-9.6KG=0.4KG$.

Mathematically, it can be described by the formula given below,

$ (\Delta X)=X_i-X$, where $ X_i$ is the measurement quantity by the device used and $X$ is the true value.

It is possible that the measurement device may either little more or a little lower than the true value, the formula can be described in absolute form, that is

$$(\Delta X)=|X_i-X| $$

Note that

- If someones know the true value and the measured value, then the absolute error of measurement is just the subtraction of these numbers. However, sometimes, one may not know about the true value, one should use the maximum possible error as the absolute error.
- Any possible measurement that one makes is an approximation, 100% accuracy of any measurement is impossible. It is also possible that if a measurement is of the same object is made twice, then the two measurements may not be identical. Such differences between measurements (of the same object) are called a variation in the measurement.
- The absolute error of measurement does not provide any details about the graveness or importance of the error. For example, when measuring the distances between cities Kilometers apart , an error of few centimeters is negligible. However, an error of centimeters when measuring a small piece of a machine is a significant error.
- The largest possible absolute error of a measurement is always half of the value of the smallest unit used.