I think it's a simple conversion of specific capacitance to area specific capacitance.
So, if know the loading (g) of your active material just multiply that number with specific capacitance you will get the total capacitance in Farad (F). Now you divided your capacitance with area of the electrode (cm2) you will get area specific capacitance (F/cm2).
The areal capacitance of a planar electrode, where thickness is negligible compared to the width and height ( for thin film/nickel foam electrode). If you know the mass loading (gram) of your electrode. There are numerous ways to obtain capacitance of electrode ( from GCDs and CVs), and you can divide the calculated capacitance (in F) by area for arial capacitance (F cm-2).
For the conversion of specific capacitance calculated in Farad per gram (F/g) to F/cm^2, simply you can replace the mass of electrode (g) by area (cm^2) from the basic formula to calculate the capacitance.
I agree with Bapi Bera, it is as simple as knowing the mass loading with which you calculate the specific capacitance and then divide with surface area of the electrode