Fair Dice Sum Probability Calculator

How to use Fair Dice Sum Probability Calculator

Convolve integer counts for(x+x²+…+x^faces)^dice. Exact BigInt event counts divide by faces^dice; the decimal probability is an approximate representation of that exact fraction.

1. Enter dice count, faces per die, exact sum or lower inclusive sum, upper inclusive sum for range mode.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• 1–20dice,2–50faces,requested sums0–1000. Fair independent dice only; no arbitrary dice expressions, loaded-die model or profitability guarantee.
• Runs locally. Text/JSON fields are capped at30,000 characters; stricter page-specific and numeric-string limits also apply. Numeric inputs are bounded to magnitude1e15 and nonzero magnitude at least1e-100 unless an exact-string mode states otherwise. Approximate summaries use12 significant digits; CSV numeric cells retain the complete stored value and potentially formula-like string cells gain a protective apostrophe; unsupported, non-finite or detected underflow states return an error.