Free online dice roller and probability calculator

How to use

1. Choose the number of dice (1–20) and the die type (d4 through d100).
2. Enter a modifier to add or subtract from the total.
3. Optionally enter a target number to see the probability of rolling that or higher.
4. Click Roll dice to see your result and statistics.

Formulas

min  = numDice × 1 + modifier
max  = numDice × sides + modifier
mean = numDice × (sides + 1) / 2 + modifier

variance per die = (sides² − 1) / 12
total variance   = numDice × variance per die
stdDev           = √(total variance)

Single-die probability (exact):

P(roll ≥ target) = (sides − (target − modifier) + 1) / sides

Multi-die probability (normal approximation with continuity correction):

P(sum ≥ target) ≈ P(Z ≥ (target − 0.5 − mean) / stdDev)

Worked example

Rolling 2d6+3 with a target of 10:

min  = 2×1+3  = 5
max  = 2×6+3  = 15
mean = 2×3.5+3 = 10
variance = 2×(36−1)/12 = 5.833
stdDev = √5.833 ≈ 2.415

P(roll ≥ 10) ≈ P(Z ≥ (10 − 0.5 − 10) / 2.415) = P(Z ≥ −0.207) ≈ 58%

Notes

• The normal approximation is most accurate for 3 or more dice. For a single die, exact probabilities are always used.
• The d100 (percentile die) is equivalent to rolling 1d100 and produces results from 1 to 100.
• Negative modifiers can push the minimum result below zero.