onlinecalculator.me

Free online dice roller and probability calculator

A dice roller that simulates any combination of polyhedral dice and shows the statistical range of possible results. Enter a target number to see the probability of rolling that.

About this 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.

Frequently asked

How is the mean of a dice roll calculated?
The mean of rolling n dice with s sides is n × (s + 1) / 2. For 2d6 that is 2 × 7 / 2 = 7. Adding a modifier shifts the mean by the same amount.
How is the probability of reaching a target calculated?
For a single die, the probability of rolling ≥ target is (sides − target + 1) / sides — an exact calculation. For multiple dice, the calculator uses a normal approximation with continuity correction, since summing dice distributions approaches a normal curve.
What is a modifier?
A modifier is a flat number added to or subtracted from the total. In tabletop RPGs like D&D, a +3 modifier means every roll is 3 higher than the dice alone. Modifiers shift the min, max, and mean by the same fixed amount.
What does standard deviation mean for dice?
Standard deviation measures how spread out results are. A larger standard deviation means rolls vary more from the mean. For n dice with s sides, the variance per die is (s² − 1) / 12, and the total variance is n times that.
How do I share my dice configuration?
Click Share to copy the page link, or Share with my numbers to include your dice settings in the URL.

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