Capacitors are not like batteries.  They do not maintain a fixed voltage when discharged, but instead decay exponentially. Look at how an “RC” circuit discharges for an example.  So, what you really need to know is how far down that curve you can go.  Is 11 V an acceptable endpoint?  Or is 9 V?  Or do you need 11.5 V?  Once you figure that out, you should be able to find how much capacitance you need to let you stay at or above that level for 1/2 second.