Measurements of fog characteristics are rare, and therefore models for predicting the attenuation caused by fog on the propagation of electromagnetic radiation are scarce. Using experimental transmissions through moderate radiation fogs on a 500-m path, a method is developed to infer the physical characteristics of fog from concurrent attenuation measurements at millimeter, infrared, and visible wavelengths. It makes it possible to retrieve the fog drop size distribution, as well as its time evolution, during the life cycle of a fog event. It yields realistic values for fog features, such as liquid water content and average drop diameter, which are not easily measured. Furthermore, on an experimental basis, simple relationships between inferred fog characteristics and measured attenuation are proposed. It is found that while both millimetric and infrared attenuations are directly related to liquid water content, visible attenuation strongly depends on the size of the fog droplets. Overall, using these relationships together with statistical distributions of inferred fog characteristics enables predictions of fog attenuation at any wavelength from millimetric to visible.