DC motor as an electric machine have been applied in numerous control systems. However, a critical parameter of interest that must be evaluated in designing a DC motor based system is the damping constant of the rotor. This paper analytically examines how to determine the damping constant of the rotor of a 12V DC motor, with the determination based on the following parameters: Armature resistance (R a), inductance (La), Capacitance, the Stall current and the Angular rate of excitation of the motor with varying armature excitation of the current. These parameters help to ascertain the maximum and the minimum operating limit of the motor so as not to exceed the boundary-operating limits of the 12V motor. Experiments were performed in the laboratory and at the end of the analysis, the result shows that the value of damping constant of a 12V DC motor was-3.317  10-4 N-m-sec 2. This parameter can be factored in future control system designs.