In order to achieve the online automatic measurement of the radial runout of the outer ring of P4/P2 angular contact ball bearings, we proposed a relative Pneumatic driven precision measurement method and have developed an accompanying measuring device. Through finite element analysis, we assessed the influence of both motor drive and pneumatic drive on the measurement accuracy. The results show that pneumatic drive exerts a lesser influence on accuracy compared to continuous motor drive, leading us to adopt pneumatic actuation for our device. A nonlinear mathematical model of the axial vertical deviation angle, offset and radial vertical deviation angle of the bearing, as well as the measurement error, is established based on the geometric relationship between the aforementioned variables and the axis deviation of the trigonometric function transformation. The results of the numerical analysis demonstrate that when the axial vertical deviation angle is within the range of 0°~0.1°, the offset is within the range of 0~0.1 mm, and the radial vertical deviation angle is also within the aforementioned range. The maximum value of comprehensive measurement error is 7.5×10-6 times the radial runout of the outer ring. Finally, two groups of 7008C/P4 angular contact ball bearings (factory-verified outer ring radial run-out of 2, 3 μm) were employed for accuracy verification. The results indicate that the measurement repeatability is 0.3 μm.