The electronic or pneumatic multi-section and multi-probe gauges are widely used for diameter and coaxiality measurements due to their high measurement efficiency in workshops. However, their measurement accuracy is determined mainly by the manufacturing errors of the assembly coaxiality master, therefore, how to establish coaxiality measurement datum reference is the key technology. The physical coaxiality masters are expected to be the impossible "zero error datum reference". The higher manufacturing accuracy of the masters, the more expensive for their manufacturing costs. A novel mathematical method on the basis of error separation principle was proposed in order to separate the manufacturing errors of the master. The basic principle is that the eccentric error of the coaxiality master can be expressed as the first harmonic function and the ideal zero-error datum reference could be established by the mathematical method of two sampling operations in phase difference of 180° in coaxiality master for gauge initialization. This method can be called as "mathematical datum reference" for coaxiality measurement. Experimental results indicate that the coaxiality measurement results of the multi-section and multi-probe gauge by the novel mathematical method coincide with those of the three-coordinate measuring machine and the maximum difference of both is about 0.0014 mm. The new coaxiality measurement principle can separate the datum error of the coaxiality master theoretically and can improve the coaxiality measurement accuracy greatly with the common accuracy coaxiality master.