We report a fully analytical study of figure-eight passively mode-locked fiber lasers. An adapted master equation is established for the figure-eight fiber laser. It is of cubic complex Ginzburg-Landau type, in which the coefficients explicitly depend on the characteristics of the cavity. We derive stability conditions for passively mode-locked and continuous wave operations in both net positive dispersion and net negative dispersion. In the soliton regime, the duration and the pulse energy are studied. The model points out a great sensitivity of pulse characteristics on parameters of the cavity, in particular, on the orientation of the polarizing isolator, on the coupling coefficient of the fiber coupler and on the length of the nonlinear optical loop mirror.