An exact solution of the radiation force on a spherical object, when positioned on the acoustic axis of a cylindrical transducer, is provided. The solution is valid for any type of sphere of any size. The radiation force function allows the calibration of high-frequency focused ultrasound fields from radiation force measurements and expands the utility of the elastic sphere radiometer developed by Dunn et al. [Acustica 38, 58-61 (1977)]. Numeral results reveal an oscillatory behavior of the radiation force function for small spheres near the transducer surface and this behavior may present an opportunity for particle sorting based on the mechanical properties of the particle and other types of manipulation.