text: The calculation of the structure factor for cases differing from ideal polymer chains can be quite cumbersome, and sometimes impossible to complete analytically. However, when the small-angle scattering condition is met, , the sinc term can be expanded so one gets:
  and by utilising the definition of the radius of gyration:
  where the final transition utilises once again the small-angle approximation.
  We can thus approximate the scattering intensity in the small-angle regime as:
  and by plotting  vs.  , a so-called "Guinier plot", we may determine the radius of gyration from the slope of this linear curve. This measure is one of many examples of how scattering experiments of polymers can reveal basic properties of those polymer chains.