Dice Notation Calculator

About this calculator

Dice notation like “3d6+2” is shorthand used across tabletop games for “roll N dice with M sides each, then add a flat modifier K” — written generally as NdM+K. This calculator computes the statistical range of such a roll: the minimum possible result (all dice show 1, plus K), the maximum (all dice show M, plus K), and the average or expected value, which for a single fair die of M sides is (M+1)/2, scaled by N dice and offset by K.

Game designers, dungeon masters, and players of tabletop RPGs like Dungeons & Dragons and board games use dice notation constantly to describe damage rolls, ability checks, and random loot tables, and knowing a roll's average and spread helps with game balancing — a weapon dealing “2d6” damage has the same average as one dealing a flat “7” but with much more variance, which matters for both game design and in-the-moment player decisions.