Hello - I apologize if this question has already been posted, but a 30 minute google search on my part yielded no answers.

For the Arcane Trickster, do you in fact gain the extra dice of damage on cantrips when hitting 5th, 11th, and 17th Rogue levels? Or do you simply have the 1d8/d6/whatever regardless of your Rogue level? Or somewhere in between, perhaps?

Any insight much appreciated! Thank you!

Cantrips are based on character level not class level. So if you have the cantrip let's say Fire Bolt, be it from a class, race, item, random lulz or whatever you increase it to 2d10 damage when you reach character level 5, and so on.

So you do get it regardless then? And even for multiclassers, if I'm reading that right! That seems really powerful...

Yes.

It's actually not that powerful. For example, a Fighter focusing on strength will have a minimum +3 Strength Mod by level 5 going by standard array or point buy. They have a Battleaxe they wield two-handed (1d10) and at level 5 they get to attack twice. So this is 1d10+3 twice or 2d10+6 overall if they hit with both. The average result of 1d10 is 5 (actually 5.5 and most would round up, but let's round down for argument's sake). This is an average of 16 damage each turn. Using Fire Bolt you just do the 2d10 or 10 damage. You may be able to find a way to improve this with Evoker Wizard or a Dragon Sorcerer but the most is 13 damage.

Now add that other class features and yeah, cantrips are not powerful really.

Also realise that as an Arcane Trickster you cannot get sneak attack on a spell. You only get sneak attack on a weapon hit. Attack cantrips are not very good for Arcane Tricksters as they could use weapons to get better damage output.

As a 5th level Arcane Trickster you see your enemy is wounded, not heavily so, but certainly taken some hits. Now, you could grind further with 2d10 at best fire bolt OR you could try Sleep 1st level spell and if you roll high enough you might get to knock them out. You can then spend your next turn going to them, stabbing them, disengaging and getting away and repeating the process. Why is this better? A melee attack against a sleeping target is made with advantage, so you would get sneak attack, and it is considered an automatic critical meaning if you hit you roll all the damage die twice including your sneak attack. Let's say you used a Shortsword, 1d6, your sneak attack is 3d6 so that is 4d6 twice or 8d6 the average for this is 28 damage and you add your dexterity mod on top of this. And you have another 2 more spell slots for casting sleep again, each one becoming easier to succeed with. So... How much more powerful is that Fire Bolt in battle?

Cantrips even with their scaling on character level is small potatoes compared to weapons as used by martial classes or spell combos used by spellcasting. The only exception is a warlock with Eldritch Blast. Cantrips are not powerful, not even slightly. They're used for pacing yourself through smaller fights or utility not for any real damage output compared to other class abilities.

Quote from Cyb3rM1nd >>

Yes.

It's actually not that powerful. For example, a Fighter focusing on strength will have a minimum +3 Strength Mod by level 5 going by standard array or point buy. They have a Battleaxe they wield two-handed (1d10) and at level 5 they get to attack twice. So this is 1d10+3 twice or 2d10+6 overall if they hit with both. The average result of 1d10 is 5 (actually 5.5 and most would round up, but let's round down for argument's sake). This is an average of 16 damage each turn. Using Fire Bolt you just do the 2d10 or 10 damage. You may be able to find a way to improve this with Evoker Wizard or a Dragon Sorcerer but the most is 13 damage.

Now add that other class features and yeah, cantrips are not powerful really.

Also realise that as an Arcane Trickster you cannot get sneak attack on a spell. You only get sneak attack on a weapon hit. Attack cantrips are not very good for Arcane Tricksters as they could use weapons to get better damage output.

As a 5th level Arcane Trickster you see your enemy is wounded, not heavily so, but certainly taken some hits. Now, you could grind further with 2d10 at best fire bolt OR you could try Sleep 1st level spell and if you roll high enough you might get to knock them out. You can then spend your next turn going to them, stabbing them, disengaging and getting away and repeating the process. Why is this better? A melee attack against a sleeping target is made with advantage, so you would get sneak attack, and it is considered an automatic critical meaning if you hit you roll all the damage die twice including your sneak attack. Let's say you used a Shortsword, 1d6, your sneak attack is 3d6 so that is 4d6 twice or 8d6 the average for this is 28 damage and you add your dexterity mod on top of this. And you have another 2 more spell slots for casting sleep again, each one becoming easier to succeed with. So... How much more powerful is that Fire Bolt in battle?

Cantrips even with their scaling on character level is small potatoes compared to weapons as used by martial classes or spell combos used by spellcasting. The only exception is a warlock with Eldritch Blast. Cantrips are not powerful, not even slightly. They're used for pacing yourself through smaller fights or utility not for any real damage output compared to other class abilities.

That is because those spells require you to make a weapon attack, which, as I did in fact say, you need for a sneak attack. It is very clear that I was saying spells like Fire Bolt do not grant sneak attack.

But like I was saying @CPrice91 it would be a good idea to get one or the other if you use melee. If your DM allows it, I'd also suggest checking out the melee cantrips in Eleminster's Guide to Magic on Dungeon Masters Guild.

Cantrips do have an advantage over melee, even for Rogues: ranged magic damage.  Sure, Rogues can get range from ranged weapons, but a) they'd need to switch weapons, and b) it's still slashing/piercing/bludgeoning damage.  Against a target with resistance or immunity to these, cantrips can be a good option, especially if avoiding being in melee range is desired.