In this study an analytical solution of the Brownian coagulation equation utilizing the method given in Park et al. [(1999) J. Aerosol Sci. 30, 3-16] but using a more detailed coagulation coefficient instead of the simple approach-the harmonic mean-Park et al. [(1999) J. Aerosol Sci. 30, 3-16] is derived. Comparisons are made with the analytical solution given in Park et al. [(1999) J. Aerosol Sci. 30, 3-16], with a method of moments model, with a log-normal reference model as well as with a sectional model (Landgrebe and Pratsinis, (1990) J. Colloid Interface Sci. 139, 63-86). In order to make a fair comparison between the models, all of them should use the same coagulation coefficients except Park et al. [(1999) J. Aerosol Sci. 30, 3-16] which is already fixed to the harmonic mean method. The most frequently used coagulation coefficients to describe the process of Brownian coagulation in the entire size regime (Fuchs, Dahneke, harmonic mean) were compared and a universal enhancement function to the near-continuum coagulation kernel is given. Furthermore, Fuchs' coagulation kernel is reviewed and modified for the use with different sized particles. It was shown that Dahneke's coagulation kernel is very close to those of Fuchs and Wright with a relative error of less than 1%. Based on this finding, Dahneke's coagulation kernel is used in the models developed as well as during the comparison. In order to develop fast and easy-to-use coagulation models we used the moment method assuming a log-normal size distribution function [Lee et al., (1997), J. Colloid Interface Sci. 188, 486-492]. In the first step the integrals over the particle size distribution are solved analytically and DGEAR (IMSL, 1980)is used to solve for the time dependence. In the second step we solved also the time dependence of the parameters of the size distribution analytically. The models developed are compared over a wide parameter range with a reference model based on the moment method of log-normal size distribution functions as well as a sectional reference model. For a worst case, the moment method shows a relative error of less than 4% for the number concentration; the mean geometric standard deviation and the volume square concentration and for the geometric standard deviation the relative error is less than 8% in the self-preserving state. The analytical solution developed shows a maximum relative error of less than 10% if the dimensionless time is limited to K(co)N(o)t = 1.