This paper describes the goniometric calibration of the spatial RI imaging telescope (SPIRIT) III. The SPIRIT III radiometer is the primary instrument aboard the Midcourse Space Experiment (MSX) satellite which was launched on 24 April, 1996. The sensor consists of an off-axis reimaging telescope with a six-band scanning radiometer that covers the spectrum from midwave IR to longwave IR. The radiometer has five arsenic-doped silicon focal plane detector arrays which operate at temperatures between 11 and 13 K. These arrays consists of 8 by 192 pixels, with an angular separation between adjacent pixels of approximately 90 (mu) rad. A single axis scan mirror can either remain fixed, or operate at a constant 0.46 deg/sec scan rate to give programmable fields of regard of 1 by 0.75, 1 by 1.5, and 1 by 3 degrees. The calibration, which is based on a physical model of the sensor, uses ground and on-orbit observations to determine and separate effects of scan-mirror encoder non-linearity, scan-mirror readout timing and angular velocity, detector readout timing, array coalignment, and optical distortion. This paper describes the calibration methodology and gives results using observations of stellar sources acquired during on-orbit operations.