How to calculate how long a supercap can provide power
Hold up time is 

T= \$\frac{C(V_s - V_f)}{I}\$ 

where I is the current, C is the capacitance, Vs is initial voltage on the capacitor, Vf is final voltage on the capacitor (perhaps the minimum voltage at which the system will work). 

That's for an ideal capacitor. If the capacitor has significant internal resistance the voltage will drop an additional amount I*R, so the hold up time will be reduced. For a non-ideal capacitor, also adjust I to add the internal leakage current. 

If you're trying to hold up a RPi long enough for an orderly shutdown I think you're going to require a very large supercapacitor with low internal resistance or a battery.