Radiation portal monitor (RPM) systems are widely used at international border crossings, where they are applied to the task of detecting nuclear devices, special nuclear material, and radiation dispersal device materials that could appear at borders. The requirements and constraints on RPM systems deployed at high-volume border crossings are significantly different from those at weapons facilities or steel recycling plants, the former being required to rapidly detect localized sources of radiation with a very high detection probability and low false-alarm rate, while screening all of the traffic without impeding the flow of commerce [Chambers, W.H., Atwater, H.F., Fehlau, P.E., Hastings, R.D., Henry, C.N., Kunz, W.E., Sampson, T.E., Whittlesey, T.H., Worth, G.M., 1974. Portal Monitor for Diversion Safeguards. LA-5681, Los Alamos Scientific Laboratory, Los Alamos, NM]. In the present work, compact analytical formulae are derived and used to calibrate two RPM systems with isotropic radiating sources: (i) polyvinyltoluene (PVT) or plastic and (ii) thallium-doped crystalline sodium iodide, NaI(Tl), gamma-ray detector materials. The calculated efficiencies are compared to measured values reported in the literatures, showing very good agreement.