© 2016 Author(s). In this paper, we present a novel method for analyzing electrohydrodynamic (EHD) thrusters. The method is based on a perturbation technique applied to a set of drift-diffusion equations, similar to the one introduced in our previous study on estimating breakdown voltage. The thrust-to-current ratio is generalized to represent the performance of EHD thrusters. We have compared the thrust-to-current ratio obtained theoretically with that obtained from the proposed method under atmospheric air conditions, and we have obtained good quantitative agreement. Also, we have conducted a numerical simulation in more complex thruster geometries, such as the dual-stage thruster developed by Masuyama and Barrett [Proc. R. Soc. A 469, 20120623 (2013)]. We quantitatively clarify the fact that if the magnitude of a third electrode voltage is low, the effective gap distance shortens, whereas if the magnitude of the third electrode voltage is sufficiently high, the effective gap distance lengthens.