Dice probabilities

Enter NdY with an optional signed modifier, for example 2d6+1. N independent fair dice have faces 1 through Y; the modifier is added once to the total, not to each die. Choose at least, exactly or at most, set an integer target and Calculate. Spaces and uppercase D are accepted. Rerolls, exploding dice and dropping/keeping dice are not supported.

All ordered outcomes are counted with exact integers by convolution. Percentages are rounded and use scientific notation for tiny nonzero chances; values close to certainty use a lower bound rather than a false 100%. Only impossible/certain events show exactly 0%/100%. Exact outcome counts shows favourable outcomes divided by all outcomes, without reducing the fraction. The mean is an average, not necessarily a possible or most likely sum.

The plot highlights the selected event. For large distributions, up to 180 bars group adjacent sums; bar height is average probability per sum and coloured area represents the matching portion. Axis values and tooltips use the current language. CSV includes every sum, its exact integer count and a rounded probability from 0 to 1, with comma-separated columns and decimal points.

Limits: 1–100 dice, 1–1000 sides and at most 10001 possible sums; modifier from −1000000000 to 1000000000 and any safe-integer target (up to ±9007199254740991). Counts are computed only when requested. Inputs remain in page memory during navigation; reloading resets them. No dice are rolled, and input is not uploaded or persisted.