The propagation equation of the effective radius of curvature of general beams in atmospheric turbulence and free space is given, and the formula of the position where the effective radius of curvature reaches its minimum is also derived. The properties of the effective radius of curvature are studied analytically, and illustrated by numerical calculation examples. It is shown that the effective radius of curvature of general beams obeys the same free-space propagation equation as the wavefront curvature of an ideal Gaussian beam. In free space the wavefront of general beams can be regarded as a spherical surface when the propagation distance is long enough. However, in turbulence the effective radius of curvature of general beams depends on the beam parameters when the propagation distance is long enough, and the effective radius of curvature decreases when the strength of turbulence-increases.