But you have asked for the minimum allowable thread depth, i.e. length of thread, to be tapped.
Wgchere is quite right, typically one diameter is full length of engagement. This is usually used in the thread programs when length of engagement is unspecified.
Otherwise you need to know the loads applied to the threading and determine length of thread based on shear. Since the internal thread profile has greater shear area than the external counterpart, and I mean always, you can base your calculation on the external threading alone.
The Machinist Handbook covers this fairly well for Acme and Stub Acme threads, not so great for Unified National and Metric edition. However, there are plenty of programs readily available to which you can apply the numbers specific to your case for a quick answer.
I'd concur with others and say one thread diameter.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada