The overlapping area of the two spectrum curves can be expressed by

Area= Integral from lambda1 to lambda2 of the multiplication of the two spectrum curves with respect to lanbda,

Area= integral S1(lambda) S2(lambda2) dlambda from lambda1 to lambda2

with lambda1 is the lower limit of the intercept and lambda2 is the higher limit of the intercept. If you do not have the intercept points you can integrate from zero to infinity.

Best wishes

Dear Morteza Zahedi

Obviously, the proposal given by Abdelhalim abdelnaby Zekry is one of many possible ways of calculating the "overlaping area". But for better fitting the expectations, the Author should provide the reason/needs of the resulting parameter. Let me present some [quessed] simple possibility of the goal of such calculations: If the first spectrum is the one of the light generated by a lamp used for - say exciting a luminescent medium, and if the other spectrum is the so called absorption spectrum of the illuminated substance, then indeed the product might be descriptive for the effectiveness of the energy absorption. HOWEVER, the units should be somehow adjusted, e.g. by division of the integral of the absorption spectrum. Then, if the emitter spectrum is in units Energy/WaveLength and the integral is wrt to Wavelength (\lambda), then the result (after division) will be in the units of Energy. This is just for illustrative reason presented in simple circumstances (e.g. without taking into accout the spatial distribution of the radiation). Usually the operations on the integral are much more complex due to the configuration of the objects: are there some collimators or not, is the absorber dissolved in a transparent fluid or non-transparent (then - how about the thickeness), ETC.ETC. Thus the problem requires further search of the phenomena accompanying the experimental setting(s).

Best regards,

Joachim Domsta

You have to add vectors at every frequency point of the spectrum.