Estimating the dynamic state variables of a synchronous generator has been a long standing research problem in power system control designs. In this paper, we present a technique to compute approximately the state variables of a synchronous generator, purely from terminal measurements. The approximation follows from an analysis of the fundamental equations describing synchronous machine models. The method assumes the availablity of the measurements: real and reactive power, terminal voltage, and the field current. By exploiting the structure of the flux linkage equations, approximate formulas for the machine rotor angle (with respect to the phase of the terminal voltage) as well as for the internal flux linkages are derived, and they are shown to be excellent approximations in simulations of detailed machine models.