The absolute measurement of hydrogen and hydrogen isotope concentrations in materials is of interest to many areas of both applied and fundamental research. In this work we describe a technique for the high accuracy determination of hydrogen concentration in thin films. The technique involves the thermal desorption of hydrogen from the film at a temperature of 900°C. Application of the ideal gas law to such experiments is questionable at best due to the extreme temperature range existing between the thermal desorption system and the mass spectrometer inlet system. To overcome issues associated with such extremes in temperature we use a response function technique to quantitate the total molar quantity of gas evolved from the film followed by high resolution mass spectrometric determination of the constituent components. Molar concentrations in the range 10@super-8@ to 10@super-5@ are routinely determined to an overall uncertainty of ±1%.