Does the Rogue have to declare that they're using Uncanny Dodge before or after damage is rolled? [duplicate]

Question

I've played a Rogue character in a few campaigns. At level 5, Rogues gain the Uncanny Dodge feature, described as follows:

Starting at 5th level, when an attacker that you can see hits you with an attack, you can use your reaction to halve the attack’s damage against you.

In practice, this has never been an issue, as my DMs have always allowed me to choose whether to use Uncanny Dodge after damage has been rolled... But I recently came across someone asking whether it had to be done before or after damage was rolled, and I realized I wasn't sure.

So obviously, Uncanny Dodge can only be used after a successful attack roll by the enemy, but according to the rules, does Uncanny Dodge have to be decided upon before or after damage is rolled? (Both RAW and RAI answers are welcome as long as they are properly supported.)

Answer 1

Before the damage roll

Attack-related options can trigger on 3 things:

• Being attacked (like the Protection fighting style)
• Being hit (like Uncanny Dodge)
• Being damaged (like Misty Escape)

Compare the wordings:

Uncanny Dodge:

when an attacker that you can see hits you with an attack

Misty Escape (Warlock 6, PHB p109)

When you take damage

Answer 2

It’s not definite so each DM has to decide for themselves.

Compare “when an attacker ... hits you with an attack” with “On a hit, you roll damage, ...”. Effectively, they are contemporaneous.