Cross sections commonly calculated using Mie theory include efficiency coefficients for extinction , scattering , and Absorption  cross sections. These are normalized by the geometrical cross sections of the particle  as 
The cross section is defined by 
where  is the energy flow through the surrounding surface, and  is the intensity of the incident wave. For a plane wave the intensity is going to be , where  is the impedance of the host medium.
The main approach is based on the following. Firstly, we construct an imaginary sphere of radius  (surface ) around the particle (the scatterer). The net rate of electromagnetic energy crosses the surface  is
where  is the time averaged Poynting vector. If  energy is absorbed within the sphere, otherwise energy is being created within the sphere. We will not consider this case here. If the host medium is non-absorbing, the energy must be absorbed by the particle. We decompose the total field into incident and scattered parts , and the same for the magnetic field . Thus, we can decompose  into the three terms , where
Where , , and . 
All the field can be decomposed into the series of vector spherical harmonics (VSH). After that, all the integrals can be taken.
In the case of a uniform sphere of radius , permittivity , and permeability  the problem has a precise solution.  The scattering and extinction coefficients are