Relative and absolute error: definitions and differences

No physical quantity can be measured exactly. Each time, making any measurement and naming the result, one can judge the absolute accuracy of the obtained value with only a certain probability. And the value of this probability is negligible because any measured value enters a certain interval, which determines the absolute error.

In general, the error is the deviation of the obtained value of the measured value from its true value. The realities of the world around us are such that no instrument, no matter how precise it is, can not communicate an absolutely precise meaning. Therefore, during measurement, it is said that the absolute error has formed a certain interval, and in the interval between its boundaries the measured value is located.

How is the interval in which the true value of the measured value is located? The first parameter is the accuracy of the device. Depending on the technology of manufacturing the measuring instrument, its properties and characteristics, this or that error value arises. Of course, the higher the accuracy of the instrument, other things being equal, the more expensive it is, but the more accurate measurement result it provides to the observer. The choice of measuring means and its accuracy depends on the requirements of the problem being solved. Not all calculations require high accuracy, and therefore it is important to correctly select the device in such a way that the results obtained do not influence the overall result of the measurement.

Another parameter that affects the accuracy is the correctness of using the measuring device. And it plays a very important role in the measurement! Any person who conducts measurements must be able to correctly handle the measurement tool. Otherwise, he runs the risk of not only getting incorrect results, but even ruining the device. Therefore, before using the measuring instrument (especially high-tech) it is important to read the instruction, understand the operating principle and the device configuration scheme,

And only then proceed to the measurements.

The third parameter is the direct reading of the instruments. If the device is equipped with a digital display, then the absolute error by this criterion is zero. In the case where the instrument has a measuring scale, the measurement error increases, since The observer can simply incorrectly take the testimony due to the physiological features of the person's vision. As a rule, in such cases, the error interval increases by the unit division price.

The last key parameter is related to the method of processing the measurement. And first of all it depends on the correctness of the rounding of the received value. It should be noted that any rounding already initially distorts the true value, but again, when carrying out the results processing procedure, it is important to consider what effect the application of this or that method of value processing has on the truth of the solution of the problem.

The four parameters listed above are only external, most obvious factors that influence the formation of the interval of deviation of the received value from the real one. In fact, the absolute error depends on a set of parameters that, depending on the type of problem, the effect of the medium, the type of instrument used, can have a tremendous impact on the measurement results.

In conclusion, we note how the relative and absolute errors are interrelated. The first is the ratio of the magnitude of the absolute error to the measured value. Therefore, if the absolute error is a certain value with the same dimension as the measured value, then the relative error shows how much the error is from the true result of the value.