The properties of calibration spheres made from electrical?grade copper, denoted Cu, and tungsten carbide with 6% cobalt binder, denoted WC, are examined theoretically. Effects of variations in material, medium, and equipment parameters are determined for spheres intended to calibrate 38?kHz echo sounders when a target strength of order ?41.5 dB is required. The derived 30.4?mm?diam Cu sphere and selected 38.1?mm?diam WC ball bearing show different dependences on the varied parameters. Changes in the material and equipment parameters within wide ranges will not upset a precision calibration with expected ±0.1?dB accuracy. Adjustment of the calibration value of ?backscattering cross section with changing temperature is generally necessary for elastic spheres. This is the case for the present WC sphere, but not for the Cu sphere by virtue of its optimization with respect to temperature. Greater hardness is found to be insufficient for choosing between the two; the particular application must be considered. Pragmatic criteria for sphere selection are discussed.