Thermal desorption is described by the Polanyi–Wigner equation derived from the Arrhenius equation.
where 
: the desorption rate [mol/(cm s)] as a function of ,
: order of desorption,
: surface coverage,
: pre-exponential factor [Hz] as a function of ,
: activation energy of desorption [kJ/mol] as a function of ,
: gas constant [J/(K mol)],
: temperature [K].
This equation is difficult in practice while several variables are a function of the coverage and influence each other. The “complete analysis method” calculates the pre-exponential factor and the activation energy at several coverages. This calculation can be simplified. First we assume the pre-exponential factor and the activation energy to be independent of the coverage.
We also assume a linear heating rate:
<br />
(equation 1)
where:
: the heating rate in [K/s],
: the start temperature in [K],
: the time in [s].
We assume that the pump rate of the system is indefinitely large, thus no gasses will absorb during the desorption. The change in pressure during desorption is described as:
<br />
(equation 2) 
where:
: the pressure in the system,
: the time in [s].
: the sample surface [m],
: a constant,
: volume of the system [m],
: the desorption rate [mol/(cm s)],
: the pump rate,
: volume of the system [m],
We assume that  is indefinitely large so molecules do not re-adsorp during desorption process and we assume that 
where: 
: the desorption rate[mol/(cm s)],
: order of desorption,
: surface coverage,
: pre-exponential factor [Hz],
: activation energy of desorption [kJ/mol],
: gas constant,
: temperature [K].
Using the before mentioned Redhead method (a method less precise as the "complete analysis" or the "leading edge" method) and the temperature maximum  one can determine the activation energy:
<br />
(equation 5)
<br />	
for n=1 
<br />
(equation  6)
<br />	
for n=2
M. Ehasi and K. Christmann described a simple method to determine the activation energy of the second order.
Equation 6 can be changed into:
<br />
(equation  6a)
where:
 is the surface area of a TDS or TPD peak.
A graph of  versus  results in a straight line with a slope equal to .
Thus in a first-order reaction the  is independent of the surface coverage. Changing the surface coverage one can determine . Usually a fixed value of the pre-exponential factor is used and is  known, with these values one can derive the  iteratively from .