You will not necessary need to know the type of particles that you have. However, you should have sufficient data in the porod regime I(q)~q-4
You can use equations 2.1b with 2.1a (page 16) of the sasfit manual see sasfit.pdf
The only issue is that you perform a numerical integration of q2·I(q) from 0 to infinity in order to calculate the invariant. To obtain an accurate value of the invariant it is better to use guinier an Porods law in order to approximate the contribution of the scattering intensity outside the measured regimes, see "How to calculate invariant over full q-regime.pdf"
Then you can use equation 2.1b to calculate the surface to volume ratio. Note that, if your data have a proper Porod regime the trend q4 · I(q) should be roughly horizontal. Then the limit q → ∞ of I(q) · q4 ≈ IqH· (qH)4 , where qH is the highest measured q-value and IqH is the scattering intensity at qH
Moreover you should be careful what you are probing. If you measure a porod regime roughly above q = 10 nm-1 you are probing the surface of individual electron rich atoms instead of a "true surface".
this is an interesting question, but to give a more accurate answer it is important to know what kind of scattering particles are you talking about. for instance, for globular proteins you can use the methods explained by Rogier and Mahadi, but if you have micelles, or some heterogenic scattering particle, it is a different way to deal with it... Besides, there are several deeper SAXS data analysis that you can use to get richer information on the scattering particle, why is the surface per volume important for you? here, i attached a chapter (there are several of them!) talking about the SAXS methodologies to study proteins in solution...
A plot of q4·I(q) versus q4 (Porod-Debye plot) displays a plateau or a curve that asymptotically approaches a constant value. The amplitude of the asymptote is proportional to the particle’s surface-area-to-volume ratio and concentration. You can find these methods in our review you can download from my papers in ResearrchGate -Super-resolution in solution X-ray scattering and its applications to structural systems biology. Rambo RP, Tainer JA. Annu Rev Biophys. 2013;42:415-41. You may also want to look at the tutorials in http://www.bioisis.net .