By extending the Gaussian gravitational flux theory, it is shown that the inertia of an accelerating object is proportional to the flux of its positional uncertainty in space. The constant of proportionality is found to be c/A where  is the density of the object, c is the speed of light and A is the diameter of the smallest possible black hole in nature - itself another constant of nature. In the case of a rectilinear acceleration, the proposed quantum formulation leads to F_I= -Ma. In the case of a rotational acceleration, the formulation leads to the rotational inertia T_I =-I dΩ/dt; both cases consistent with the predictions of the classical mechanics. In the case of a disc spinning under a constant rotational velocity Ω, the inertia resulting from the centripetal uncertainty of its constituents is found to reduce to T_I = -2/3 M R Ω^2, again identical to that of the classical mechanics. The latter, however, is found to be an underestimation of the actual quantum-relativistic solution wherein RΩ is non-negligible compared to c.