The input admittance of an elemental radiator on a curved surface, e.g. a slot on a cone, plays an important role in the design of conformal arrays. A search through the literature reveals that, at present, there is no reliable theoretical method available for computing this admittance. The objective of this paper is to provide a solution to this problem using a surface-ray approach–within the framework of g.t.d. The solution is verified for the limiting case where the cone degenerates into a cylinder, and it is shown that the g.t.d. results compare extremely well with the exact modal solution to the cylinder problem. Extensive numerical results are presented in the paper for the input admittance of a cone as a function of various design parameters.