We present an electromagnetic design of 325 MHz superconducting single-spoke resonators (SSRs) to accelerate the H$^−$ ions from 3 to ∼160 MeV for the proposed Indian Facility for Spallation Research project. The geometrical parameters of SSRs have been optimised to maximise the achievable acceleration gradient, and to minimise the multipacting growth rate, keeping a reasonably low value of heat dissipation on the cavity surface. For the geometrical optimisation of SSR cavities, we followed a one-dimensional procedure, where we vary and fix the geometrical parameters one by one in a sequential manner. We explain the behaviour of various RF parameters of the SSR with respect to its geometrical parameters, based on which the optimum value of each of the geometricalparameters has been chosen. For the optimised geometry of SSRs, we performed the higher-order mode (HOM) analysis and estimated the transverse and longitudinal kicks imparted to the beam by HOMs. The effect of azimuthala symmetry of the electromagnetic field is also analysed and presented for the adopted design. A holistic design approach is described in the paper that addresses the interlinked optimisation requirements.