I've heard also that the input voltage plays a part too. I remember years ago in EC&M magazine they had an article about poco's upgrading line voltage (usually doubling the voltage) which affected the available fault current, and services that previously had sufficient aic ratings, no longer would be sufficient.

The fault current calculator that I linked, assumes "infinite bus" on the utility side of the transformer, which means the product of fault current and voltage on the utility side is infinite.

Examine the formula behind fault current across a transformer, and you'll notice that V_primary * Isc_primary come as a pair, multiplied together. Call this value X. If you graph Isc_secondary as a function of X, you will notice that there is a limit of this function, as the input approaches infinity. That is what the fault current calculator is providing. The upper limit of what the secondary fault current could be, regardless of what it starts at, before the service transformer. This feature of a function/graph is called an asymptote. This provides an upper bound on your fault current, as long as your service transformer remains unchanged, that covers you no matter what the utility does on their transmission and distribution system to adapt to the growth of other services.

The source formulas are here, in the section titled "Calculation of Short-Circuit Currents When Primary Available Short-Circuit Current is Known":

Here's an example, given the following specs:

100 kVA, 1-phase 240V, 2.5%Z, 13.8kV primary