This article describes the derivation of the efficiency for the Knudsen pump for two cases. First, by neglecting the thermal losses to calculate the maximum efficiency, and second, by including the thermal losses along the length of the channel. The Knudsen pump is a thermally driven pump with no moving parts and which functions on the principle of thermal transpiration. Diffusion is the main mode of mass transport, as opposed to bulk fluid motion. The pump functions when the gases are in a rarefied state. The efficiency without thermal losses is shown to asymptotically approach the value of the ideal gas constant divided by the specific heat capacity, while the efficiency with thermal losses is given for rectangular and circular cross sections and is shown to be independent of length.