It has long been acknowledged that the well known and frequently used stability criterion beta(p)< 0.3 for the toroidal ideal magnetohydrodynamic internal kink mode in a tokamak is inaccurate for an empirically relevant safety factor. The present paper outlines the severity of the usual approximation, and presents improved analytical approximations of the general solution in M. N. Bussac, R. Pellat, D. Edery, and J. L. Soule, Phys. Rev. Lett. 35, 1638 (1975), thus providing new insights into the nature of the instability, together with simple formulas that can be incorporated into transport codes with sawtooth cycle algorithms. (C) 2007 American Institute of Physics.