An explicit formulation is presented to determine widths of magnetic island separatrices generated by magnetic field perturbations in a general toroidal stellarator geometry. The method, which is based on a representation of three-dimensional flux surfaces by double Fourier series, allows rapid and accurate calculation of the island widths in real vacuum field configurations, without the need to follow field lines through numerical integration of the field line equations. The procedure does not involve any simplifying approximations and can be used for fields with multiple small perturbations. Numerical results of the island width obtained in the flux co-ordinate representation for the Advanced Toroidal Facility agree closely with those determined from Poincaré puncture points obtained by following field lines. The effects of resonance coupling are analysed.