We examine the correspondence between various models describing flat-top laser beam profiles using two standard parameters; namely, the M² factor and the kurtosis parameter. Numerical expressions for M², based on the second moment of the beam irradiance distribution in the near and far fields and for the kurtosis parameter, k, based on the fourth moment at the near field, are obtained. Plots of k in the near field versus M² demonstrate the similarities between the different analytical models used to describe flat-top profiles. Using the Padé approximation, a relationship between k and M², a new reference formula, is derived that predicts the values of M² to within less than a percent for these flattened beams. This method is then extended to define numerical expressions relating the beam parameters (i.e., M² and k) and the parameters describing the beam characteristic in each analytical model (model parameters). The results obtained using the Padé method are used to describe the output beam profiles for a high power copper vapour laser fitted with an unstable resonator.