Abstract: There is such phenomenon in the calculation of dimensional chains that upper deviations may be smaller than lower deviations (negative tolerance). The essential difference between positive and negative numbers is that the amounts they represent has opposite meanings and the opposite meaning amount of the allowable error amount of the dimensions is the error amount of compensate dimensions. Based on the two concepts and the allowable error amounts of the dimension of the tolerance dimensions, the explanation of the negative tolerance was given. Then the range of the tolerance was extended to any real number from the positive number, and the error compensation amounts and ranges were included in the category of tolerance control and described in a digitalized way, which met the requirement of the new generation of GPS tolerance system. The synchronous calculation of tolerances of dimensions and error compensation amounts in assembly dimensional chains can be realized when the explanation of the negative tolerance is given. This makes it more convenient to use computer assisting the design of tolerances, and it also makes the calculations of the tolerance of assembly dimensional chains with compensation components more precisely with the probabilistic method.