Given these assumptions, the flux of oxidant through each of the three phases can be expressed in terms of concentrations, material properties, and temperature.
By setting the three fluxes equal to each other  the following relations can be derived: 
Assuming a diffusion controlled growth i.e. where  determines the growth rate, and substituting  and  in terms of  from the above two relations into  and  equation respectively, one obtains:
If N is the concentration of the oxidant inside a unit volume of the oxide, then the oxide growth rate can be written in the form of a differential equation. The solution to this equation gives the oxide thickness at any time t.
where the constants  and  encapsulate the properties of the reaction and the oxide layer respectively, and  is the initial layer of oxide that was present at the surface. These constants are given as:
where , with  being the gas solubility parameter of the Henry's law and  is the partial pressure of the diffusing gas. 
Solving the quadratic equation for x yields:
Taking the short and long time limits of the above equation reveals two main modes of operation. The first mode, where the growth is linear, occurs initially when  is small. The second mode gives a quadratic growth and occurs when the oxide thickens as the oxidation time increases.
The quantities B and B/A are often called the quadratic and linear reaction rate constants.  They depend exponentially on temperature, like this:
where  is the activation energy and  is the Boltzmann constant in eV.   differs from one equation to the other.  The following table lists the values of the four parameters for single-crystal silicon under conditions typically used in industry (low doping, atmospheric pressure).  The linear rate constant depends on the orientation of the crystal (usually indicated by the Miller indices of the crystal plane facing the surface).  The table gives values for  and  silicon.