The Presbyterian-University Hospital of Pittsburgh installed the first clinically designated Leksell gamma knife in the U.S. in August 1987. Gamma knife radiosurgery involves stereotactic target localization with the Leksell frame and subsequent closed-skull single-treatment session irradiation of a lesion with multiple highly focused gamma ray beams produced from 60Co sources. The hemispherical array of sources, the large number of small-diameter beams, and the steep dose gradients surrounding a targeted lesion make physical characterization of the radiation field complex. This paper describes the physical features and the operation of the gamma knife as well as the calibration procedures of the very small, well-collimated beams. The results of studies using in-phantom ion chamber, diode, film, and lithium fluoride thermoluminescent dosimetry were all in close agreement. Both single-beam and multiple-beam dose profiles were measured and reported for the interchangeable helmets, which have 4-, 8-, 14-, and 18-mm-diameter collimators. We also describe the dose calculation and treatment planning algorithm in the treatment planning system. Measurements of the accuracy of mechanical and radiation alignment are also performed and discussed.