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The Draconic Bloodline sorcerer's 6th-level feature, Elemental Affinity, lets you add your Charisma modifier to the damage when you cast a spell. Does this count with cantrips such as fire bolt?

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Yes it does, because cantrips are spells

Specifically, cantrips are 0th level spells. From the PHB:

Every spell has a level from 0 to 9. A spell's level is a general indicator of how powerful it is, with the lowly (but still impressive) magic missile at 1st level and the earth-shaking wish at 9th. Cantrips - simple but powerful spells that characters can cast almost by rote - are level 0.

Since cantrips are spells, and Elemental Affinity lets you add your Cha mod to damage when you cast a spell, Elemental Affinity applies to cantrips (that deal the appropriate type of elemental damage, of course).

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    \$\begingroup\$ You might add that there is a specific piece of rules language it uses when it means 'spells but not cantrips', where it'll say "a spell of level 1 or higher" (or some such thing, I don't have my book at the moment). \$\endgroup\$ – Darth Pseudonym Nov 27 '18 at 21:06

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