The difference between the true value of a quantity and the value obtained by measurement. The two main types of error are random errors and systematic errors.
In any measurement there is a random error, which arises when the experimenter has to make an estimate in the last figure of the measurement, i.e. when the instrument is at the limit of its accuracy. Random errors of this type can be analysed, using statistics; for this reason they are sometimes called statistical errors. Thus, for this type of error repeating the measurement can improve the accuracy of the quantity being measured.
A systematic error cannot be analysed using statistics, however, as it results from an incorrect calibration of the measuring instrument or an incorrect position of the zero point. Repeating the experiment in these cirumstances, will not improve the accuracy of the measurement.
In quantum mechanics, the product of the uncertainties of certain quantities, such as the position and momentum of a particle, cannot be eliminated or reduced beyond the limit given by the Heisenberg uncertainty principle.