A spellcaster with 6 temporary hit points is hit for 3 damage. Do they have to make a concentration check?
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Yes (Likely).
According to 5e designer and official rules expert Jeremy Crawford, "When temporary hit points absorb damage for you, you're still taking damage, just not to your real hit points."
On 25 August 2014, Crawford was asked about a similar situation over twitter by @Mathew_Reuther:
@JeremyECrawford If my Temporary Hit Points are 10 and I take 30 damage from an attack, what is the DC of my Concentration Check?
Crawford answered:
@Mathew_Reuther The DC is 15. When temporary hit points absorb damage for you, you're still taking damage, just not to your real hit points.
For a Concentration check, "DC equals 10 or half the damage you take, whichever number is higher," so in the above twitter example, DC 15 is based on 30 damage. (PBR, p. 80; PHB, p. 203) While this situation is not exactly on point since the character took real damage on top of the temporary HP, Crawford's statement seems pretty clear that "you're still taking damage, just not to your real hit points."
However, if the actual damage was reduced altogether (not absorbed), then there would be no Concentration check. See, e.g., Deflect Missiles monk feature, Parry combat maneuver, and Heavy Armor Master feat. (PHB, pp. 74, 78 & 167)
Also, the abjurer's Arcane Ward feature has its own hit points1 and "[w]henever you take damage, the ward takes the damage instead." (PHB, p. 115) So, an attack that is wholly absorbed by the ward is not damage taken by the character and no Concentration check is needed. (Courtesy of @Dungarth)
- As opposed to giving a character temporary hit points like certain spells and magic items.
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Yes, the concentration check is required even if you have temporary hit points.
A concentration check is required in any case the caster takes damage:
The following factors can break concentration:
[...]
Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration.
There is no distinction about temporary HPs or normal HPs: the check is triggered by the damage.
This is confirmed by the Sage Advice Compendium:
If I have 10 temporary hit points and I take 30 damage from an attack while concentrating on a spell, what is the DC of the Constitution save to maintain my concentration?
The DC is 15 in that case. When temporary hit points absorb damage for you, you’re still taking damage, just not to your real hit points.
There is another entry in the SAC that indirectly confirms that even if you have temporary HPs you are still receiving damage (emphases mine):
How does Arcane Ward interact with temporary hit points and damage resistance that an abjurer might have? [...]
The ward takes damage first. Any leftover damage is taken by the wizard and goes through the following game elements in order: (1) any relevant damage immunity, (2) any relevant damage resistance, (3) any temporary hit points, and (4) real hit points.
Indeed, the wording above says that any leftover damage is taken by the wizard on the temporary HPs, if any, after having applied eventual immunities and/or resistances: the caster is hence receiving damage.
Eddymage
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2Reminder to everyone that when someone invites you to continue the discussion in chat, chat is the correct place for continuing the discussion, not comments. – Oblivious Sage Sep 22 '23 at 12:51
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There is a answer provided by sadaqah based on rules intent. My answer is instead focused on the rules as written.
No, concentration checks trigger on taking damage, but temporary hit points are a buffer against damage.
Page 198 of the PHB says about temporary hit points:
Temporary hit points aren't actual hit points; they are a buffer against damage, a pool of hit points that protect you from injury.
Losing temporary hit points does not mean you take damage.
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1I suppose then that any effect that takes damage in place of your hit points means you do not lose concentration, like the abjurer's shield. – Javelin Jan 19 '15 at 20:28
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5While THPs might not protect you from losing concentration (see @sadaqah's answer), the abjurer's ward potentially could. Indeed, the ward is not described as you getting THPs, but rather as it having its own HP pool. The ward absorbing damage does not necessarily equate to you taking damage, unlike developer's word on THPs. – Dungarth Jan 19 '15 at 21:31
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1Only the reference by sadaqah is from a reply that involved the PC being affected by the hit. So it seems to me that the magic protects you and no damage happens to yourselves and thus no concentration problems either. It makes more sense that way to me. – Alexis Wilke Jan 20 '15 at 03:19
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Since the Abjurer's ward stacks with THP, it makes sense that it is its own pool and would protect you from losing concentration regardless of THP. I would likely say that THP protect a caster as well, though either ruling works on that part. – Aviose Jan 20 '15 at 16:54
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I don't believe the answer by sadaqah was based on intent, I think it was based on an offhand tweet that wasn't given much thought - it goes against everything else in the book relating to triggered effects. You can't use Temp HP without taking damage, just like you can't cast Shield without being hit. This is not the same as actually taking damage if Temp HP absorb it all, or actually being hit if the +5AC now makes it miss. Likewise Halfling Lucky triggers if you roll a 1, but this doesn't mean you still fumbled because "you rolled a 1" (unless you roll another 1). – Tim Nov 08 '19 at 08:21
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"buffer against damage" feels like a tough call to base RAW on, as the "take damage" part of concentration is never defined more fully than that. The question then is, are you "taking damage" if the THP absorbs all of it? Feels a lot like a DM call to me, as I assume you'd still have the spell inflict any rider effects as normal, so that seems like damage was still "taken", even if it did no lasting harm. – Haravikk Aug 29 '21 at 09:39
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2Sage Advice Compendium p15 When it asks about "If I have 10 temp hp and take 30 damage what is my concentration DC"... @Haravikk – Slagmoth Sep 03 '21 at 01:11
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1Your reading of it takes temporary hit points out of context to get what you want.
If you look further into temporary hit points it still says "when you take damage". Errgo your taking damage. Your resulting hp doesn't matter where damage is concerned.
– Spoo Oct 04 '22 at 14:47
Arcane Ward: Whenever you take damage, the ward takes the damage instead. Temp HP: .. they are a buffer against damage .. When you have temporary hit points and take damage, the temporary hit points are lost first.
Both say if you would take damage, then instead deduct the damage elsewhere first. I would expect an errata if they really meant otherwise for one of them.
– Tim Nov 08 '19 at 06:18