Applications of Knudsen compressors as both microscale and macroscale vacuum pumps have been investigated. The study is based on a cascade analysis incorporating available transitional thermal transpiration and Poiseuille flow results for slender channels. It was found that the Knudsen compressor is an attractive possibility for microscale pumps down to a pressure of about 1 mTorr and for macroscale pumps to about 0.1 mTorr. A microscale pump for a micromass spectrometer providing a molecule flow rate of 5 x 10(14) molecules/s results in the following pump characteristics: energy use of 2.4 W, pump volume of 13.9 ml at an inlet pressure of 1 mTorr and an energy use of 28.5 inW, and pump volume of 0.16 ml at an inlet pressure of 10 mTorr. A macroscale pump providing a pumping speed of 10(3) l/s results in a pump with an energy use of 1786 W, and pump volume of 1695 l at an inlet pressure of 0.1 mTorr. Several; Knudsen compressor characteristics such as pressure rise, pumping speed, volume, energy use and mass flow are presented