What is the purpose of a ground in a GFCI outlet since the GFCI is just measuring the current between HOT and Neutral? Does it add any functionality or safety if it is grounded?
I've seen it suggested that a ground is not necessary, but I'd like an understanding of what capacity the ground would add (or not) to the GFCI.
(Somewhat relevant why not to connect ground to neutral)
A GFCI is one way to make an ungrounded circuit that you cannot manage to retrofit ground for safer than an otherwise unprotected ungrounded circuit.
However, it is always preferable (and required in any new work) to have an actual ground connection as well. Things fail in various ways, and if the grounding pin on a grounded item is actually connected to ground, more failure modes are protected against.
As a somewhat contrived example, if a tool with a metal shell and a grounded cord was plugged into a an ungrounded GFCI outlet but on an insulated surface, and it had a failure connecting hot to the grounded case, the case would be live, but without current flowing (it's on an insulated surface) the GFCI would not have a reason to trip until you picked it up and provided a path for current to go out of the circuit. If the GFCI works, you get a mild shock and it trips - if it fails (and they do, though more often "dead" than "alive", presumably by design) you just get shocked.
If it was grounded, either the GFCI would trip or the circuit breaker would trip. You would not be involved.
The same as a ground on a standard outlet, provide a current path from the metal chassis to ground that will be lower resistance than your body.
A GFCI will trip as soon as the sum of the AC current of live and neutral is above a threshold for longer than a specified amount of time (typically on the order of a few dozen milliamps for 16 milliseconds). However that margin leaves enough room to seriously harm someone getting the full current through them (to the point of death if the heart is involved).
The ground means that if any metal parts exposed to a person get energized the current will leak and the GFCI will trip instead of waiting until someone touches it.
Grounds have two roles.
Enhancing human safety: the GFCI pretty much takes care of that problem.
Protecting equipment: The GFCI does absolutely nothing to protect equipment from internal or external power surges, lightning, or ESD. The GFCI does not provide anywhere for surge suppressors to dump surge current. Hence the ground remains important here.
