The scattering cross section of an object () is defined by the time-averaged power of the scattered wave () divided by the intensity of the incident wave ():  .
Starting with the assumptions that a plasma object is small relative to the incident wavelength, thin relative to the skin depth, unmagnetized, and homogenous, the scattering cross-section of the plasma object can be determined by the following equation, where  is the electron charge,  is the electron mass,  is the number of unbound electrons in the plasma object,  is the geometrically-determined depolarization factor,  is the incident wave circular frequency,  is the plasma frequency, and  is the effective momentum-transfer collisional frequency (not to be confused with collisional frequency).
(The above equation is derived from the Drude-Lorentz-Sommerfeld model. It neglects transient effects of electron motion and is only qualitatively applicable to Rayleigh scattering due to neglecting evanescence effects - strict consideration of boundary conditions is often required to capture the case of negative permittivity.). The total cross section can related to the cross section of an individual electron () according to the equation , since the electron motion will be in phase assuming that the plasma object is small relative to the incident wavelength.
The scattering regime is determined by the dominant term in the denominator. Collisional scattering refers to the assumption that , allowing the total scattering cross section to be expressed as:
The collisional scattering cross-section can also be expressed in terms of the Thomson scattering cross section (), which is independent of the plasma geometry and collisional frequency according to the following equation.