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Spell save DC = 8 + your proficiency bonus + your Intelligence modifier. Spell attack modifier = your proficiency bonus + your Intelligence modifier. The attack modifier is used when making your attack roll. This is the roll to determine if your (spell) attack hits. The process is the same as for other forms of attack:
The most powerful staff in the game. +2 to spell attacks. A suite of powerful spells. An explosive destruction burst that deals more damage than literally any other attack in the game, at the possible cost of killing you instantly. I blew mine up destroying the gem that housed a Demon Lord, after he tried to take over my mind.
The proficiency bonus is in the Wizard table of PHB p113. Your Spell save DC equals 8 + proficiency bonus + Intelligence modifier. Your Spell attack modifier equals proficiency bonus + Intelligence modifier.
Yes, Cantrips get a bonus to attack. From page 205 in the PHB we have that all spells benefit: Some spells require the caster to make an attack roll to determine whether the spell effect hits the intended target. Your attack bonus with a spell attack equals your spellcasting ability modifier + your proficiency bonus.
Make a ranged spell attack against the target. On a hit, the target takes 1d10 fire damage. A flammable object hit by this spell ignites if it isn't being worn or carried. - PHB p. 242 “Spell attack” = roll a d20 and add prof and mod. Spell save means target rolls defense.
There is no specific proficiency for spell attacks. Instead, the general rule for spell attack rolls is: Your attack bonus with a spell attack equals your spellcasting ability modifier + your proficiency bonus. (PHB, p.205) So: Any character that casts a spell that requires an attack roll is "proficient", and adds their proficiency bonus. This ...
So I know how to calculate spell DC (8 + proficiency + modifier) and spell attack rolls (1d20 + proficiency + modifier), but I am not clear on spell damage. Namely, do you add your spell modifier (e.g. int for wizards) to spell damage? For example, burning hands does 3d6 fire damage or half as much if the opponent succeeds on a dex save.
The spell Bless [PHB, 219], for example, adds a d4 roll to any attack roll the target makes. So for example, a level 5 Fighter wielding a +1 Rapier (has the Finesse property), with a Strength Score of 16 and a Dexterity of 18, would have the following bonus for their Attack Roll:
When the sword appears, you make a melee spell attack against a target of your choice within 5 feet of the sword. On a hit. the target takes 3d10 force damage. Until the spell ends, you can use a bonus action on each of your turns to move the sword up to 20 feet to a spot you can see and repeat this attack against the same target or a different ...
1. Spell as bonus action, Attack as action. You could do this. Certain (very few!) spells have a casting time of "1 bonus action." As long as you meet all of the other requirements for casting such a spell, there's no reason you can't Attack as your action and cast your spell as a bonus action. (And those can happen in either order, too.)