This paper discusses a rule given in the Indian astronomical text Surya-siddhanta for computing the angular diameters of the planets. I show that this text indicates a simple formula by which the true diameters of these planets can be computed from their stated angular diameters. When these computations are carried out, they give values for the planetary diameters that agree surprisingly well with modern astronomical data. I discuss several possible explanations for this, and I suggest that the angular diameter rule in the Surya-siddhanta may be based on advanced astronomical knowledge that was developed in ancient times but has now been largely forgotten.