JAXA's Wind Tunnel Technology Center operates three Hypersonic Wind Tunnels: a 0.5 m wind tunnel (HWT1), a 1.27 m wind tunnel (HWT2), and a 0.44 m shock tunnel (HST). Hypersonic flow is generated by injecting high-temperature and high-pressure air into a vacuum chamber through a contour nozzle. To determine Mach numbers in these wind tunnels, calibration tests have been conducted using a Pitot rake. The Mach number is deduced theoretically by flow calculations based on an air model. Flow qualities, such as a dynamic pressure, Pitot pressure, static pressure, and temperature in the test section can be obtained from the Mach numbers and stagnation measurements using an air model. We have used three different air models. A perfect model is used in general for analytical purposes. A thermally perfect model was used to calibrate HWT1 and HST. A real model was applied to HWT2. This paper reports details of the three models and discusses their differences. Fortran code is supplied.