Spell Damage Calculator

Average Damage assumes no save is attempted at all, while Expected Damage weights the outcome by the target's actual chance of failing versus succeeding their save. For a spell like Fireball that deals half damage on a success, Expected Damage blends full damage on a failed save with half damage on a successful one, which is almost always lower than the flat average.

This reflects the common convention that a natural 1 on a saving throw always counts as a failure and a natural 20 always counts as a success, regardless of the actual modifiers involved — even an overwhelming save DC still leaves a 5% chance of a lucky natural 20 succeeding. This convention isn't universal across every rules variant, so check whether your table plays with or without it.

Standard critical hit rules double the number of damage dice rolled, since a crit represents an especially devastating strike in the randomized portion of the damage, but the flat modifier — representing a consistent bonus like a stat modifier — stays the same regardless of whether the hit was a critical. This is why the formula doubles dice count but adds the modifier only once.

It divides expected damage by the spell slot level required to cast it, giving a rough efficiency figure for how much damage you're getting per unit of your limited spell slot resources. A lower-level spell with a similar per-level figure to a flashier higher-level spell may actually be the more resource-efficient choice, especially across a long adventuring day with limited slots.

A higher save bonus lowers the target's failure chance, which reduces expected damage, but how much it reduces depends on whether the spell deals half damage on a save or none at all — an all-or-nothing spell's expected damage swings more dramatically with save chance than a half-on-save spell, since a half-on-save spell has a damage floor even against a near-guaranteed save.