Hi! In the absence of any external factors, the inrush current is a combination of (a) the charging of the capacitor itself under ideal conditions, which is given by the formula I = C dV/dt (capacitance multiplied by the rate at which voltage changes over time), and the cap's ESR, which basically acts as a current limiter (I = V/ESR).
External factors could be things like the presence of a current-limiting device (a resistor, for example), or practical limitations in the amount of current that the power supply can provide.
Hope this helps!
—CC