Multi-group dice calculator supporting mixed dice types (d4+d6+d20), modifiers, take highest/lowest, and batch rolls. Build any dice expression for RPGs.
Real RPG encounters rarely use just one type of die. A Paladin's Divine Smite might be 1d8 weapon damage + 2d8 radiant damage + modifier. A critical Sneak Attack could be 1d8 + 6d6. Our Dice Calculator lets you combine up to six different dice groups in a single expression, with instant results and full breakdowns.
Add multiple dice groups with different types and counts, apply a global modifier, and choose whether to sum all dice, take the single highest, or take the single lowest. Presets cover common combinations like 1d20 + 2d6 (attack + damage) and 8d6 (Fireball). Every roll shows individual results per group for complete transparency.
The built-in statistics reference table shows expected values and standard deviations for all standard dice, helping you understand the probability behind your rolls. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Complex dice expressions come up constantly in RPGs — weapon damage plus class features plus spell bonuses. Calculating these by hand is tedious and error-prone, especially during fast-paced combat. Our calculator handles any combination instantly, with a clear breakdown showing exactly which dice contributed what.
The deviation output also helps players gauge whether a roll was lucky or unlucky compared to expectations, adding context to dramatic moments.
For mixed dice NₐdSₐ + NᵦdSᵦ + M: Expected = Σ(Nᵢ × (1+Sᵢ)/2) + M. Variance = Σ(Nᵢ × (Sᵢ²−1)/12). Standard deviation = √(Total variance).
Result: 1d8 + 2d6 + 4 → [5] + [3, 6] + 4 = 18
Rolling 1d8 (weapon) + 2d6 (sneak attack) + 4 modifier. The d8 gave 5, the 2d6 gave 3 and 6, plus 4 modifier = 18 total damage. Expected: 4.5 + 7 + 4 = 15.5.
Combining different dice types creates complex probability distributions that blend the properties of each die. A 1d20 + 1d6 expression combines the flat distribution of the d20 with the more predictable d6, creating a sum with range 2-26 and a slightly curved distribution peaking around 14.
The central limit theorem means that adding more dice groups pushes the total closer to a normal distribution, regardless of the individual die shapes. A 1d4 + 1d6 + 1d8 + 1d10 + 1d12 sum is already quite bell-shaped.
Understanding dice math helps optimize character builds. Adding more dice (like Sneak Attack's escalating d6 pool) increases both average damage and consistency. Adding flat modifiers (like ability scores) increases average without reducing variance. The optimal strategy depends on whether you want reliable damage or explosive potential.
Great Weapon Fighting (reroll 1s and 2s on damage dice) is worth about +1.3 damage per d6 — knowing this helps evaluate feats and fighting styles mathematically.
The NdS notation has been extended by various VTTs and dice apps: 4d6kh3 (keep highest 3), 2d20kl1 (keep lowest 1), 1d6! (exploding), 4d6ro<3 (reroll once if under 3). While our tool uses dropdowns for clarity, understanding these notations helps when using Roll20, Foundry VTT, or similar platforms.
Yes! Add up to 6 groups, each with its own die type and count. The calculator handles 1d20 + 3d6 + 2d8 or any combination you need.
Instead of summing all dice, only the single highest result is used (plus modifier). Useful for systems like Blades in the Dark or any "best of" mechanic.
The expected value is shown automatically. Each die contributes (1+sides)/2 on average. A longsword (1d8) averages 4.5; sneak attack (4d6) averages 14.
Standard deviation measures how much your rolls typically vary from the average. Higher std dev means more swingy results. 1d12 has higher variance than 2d6 despite similar averages.
For D&D crits, just double the dice groups (e.g., 2d8 + 4d6 instead of 1d8 + 2d6). The modifier stays the same — only dice are doubled on a critical.
You can add up to 6 independent groups. Each group can have up to 100 dice of the same type.