For most purposes, it doesn't matter whether uncanny dodge happens before or after the hit.
But here's a thought experiment for you: You have five hit points. You are hit for 8 points of damage. The attack would, in general, qualify for Uncanny Dodge.
Can you use Uncanny Dodge to halve the damage? If you can, then the uncanny dodge reaction is being activated prior to the damage happening.
I would argue that "when an attacker that you can see hits you" specifies the trigger to be "hit". Not "damage". So I'd have Uncanny Dodge fire off once you know you've been hit, but before damage is rolled. That's another interesting question; do you get to wait until damage is rolled before using uncanny dodge, or do you have to decide in advance?
I'd say that, if you have to decide in advance, then the damage-halving works and after that you lose the ability to take reactions for a while. If you get to wait to see damage before deciding, it's less obvious.
But here's a thought experiment for you: You have five hit points. You are hit for 8 points of damage. The attack would, in general, qualify for Uncanny Dodge.
Can you use Uncanny Dodge to halve the damage? If you can, then the uncanny dodge reaction is being activated prior to the damage happening.
I would argue that "when an attacker that you can see hits you" specifies the trigger to be "hit". Not "damage". So I'd have Uncanny Dodge fire off once you know you've been hit, but before damage is rolled. That's another interesting question; do you get to wait until damage is rolled before using uncanny dodge, or do you have to decide in advance?
I'd say that, if you have to decide in advance, then the damage-halving works and after that you lose the ability to take reactions for a while. If you get to wait to see damage before deciding, it's less obvious.