The Burst Alert Telescope (BAT), a large coded aperture instrument with a wide field‐of‐view (FOV), provides the gamma‐ray burst triggers and locations for the Swift Gamma‐Ray Burst Explorer. In addition to providing this imaging information, BAT will perform a 15 keV – 150 keV all‐sky hard x‐ray survey based on the serendipitous pointings resulting from the study of gamma‐ray bursts, and will also monitor the sky for transient hard x‐ray sources. For BAT to provide spectral and photometric information for the gamma‐ray bursts, the transient sources and the all‐sky survey, the BAT instrument response must be determined to an increasingly greater accuracy. This paper describes the spectral models and the ground calibration experiments used to determine the BAT response to an accuracy suitable for gamma‐ray burst studies. © 2004 American Institute of Physics