Photon counting is a mode of processing astronomical observations of low-signal targets that are observed using an electron-multiplying charge-coupled device (EMCCD). In photon counting, the EMCCD amplifies the signal, and a thresholding technique effectively selects for the signal electrons while drastically reducing relative noise sources. Photometric corrections that result in the extraction of a more accurate estimate of the signal of electrons have been developed; the Nancy Grace Roman Telescope will utilize a theoretical expression for the signal-to-noise ratio (SNR) given these corrections based on well-calibrated noise parameters to plan observations taken by its coronagraph instrument. The analytic expressions for the SNR for the method of photon counting, before and after these photometric corrections are applied, are derived.