Expected Damage Roll Calculator

About this calculator

Dice notation NdS+M means rolling N dice with S sides each and adding a flat modifier M. The average (expected) result is N × (S+1)/2 + M — because each single die averages (S+1)/2 over many rolls — while the minimum is N×1+M (all dice show 1) and the maximum is N×S+M (all dice show S).

Tabletop RPG players and dungeon masters use this to estimate whether a monster's or spell's damage (like 8d6+4 for a fireball) is balanced for a given character level, and game designers use the same math to tune weapons and abilities before publishing a ruleset.