Based on the accurate definition of light intensity of nonparaxial scalar beam at the transverse plane,a detailed numerical calculation of the beam widths,far-field divergence angles,and M2 factors defined by the power in the bucket (PIB) and second-order moment are performed for nonparaxial scalar Gaussian beams,and the result is compared with that of paraxial scalar Gaussian beams.The results show that the far-field divergence angle and M2 factor defined by the PIB are less than those defined by second-order moment.Both M2 factors tend to zero as beam waists vanish.The beam widths,far-field divergence angles,and M2 factors defined by the three definitions have great differences when the parameter of beam waist w0 is relatively small,and the beam parameters tend to unity with the increasing of w0.The relationship between the beam waist parameter w0 and the validity of the second-order moment theory of paraxial and nonparaxial scalar Gaussian beams are pointed out.This will provide reference for the study of the propagation characteristics of nonparaxial beams.