The boundary element method is well suited to deal with some potential field problems encountered in the context of field emission. A boundary element method is presented in the specific case of three-dimensional problems with azimuthal symmetry. As a check, computed results are displayed for well-known theoretical examples. The code is then employed to calculate current from a field emission tip and from the same tip with a protrusion. Finally an extension of the boundary element code is employed to calculate space-charge effects on emitted current.