Dice Roller — Roll Multiple Dice with Sides & Modifiers
Roll 1–100 dice with 2–1,000 sides online for free. View each individual roll, totals, modifiers, highest and lowest rolls, and use a seed to reproduce results.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Several independent fair dice produce more combinations near the middle (for example, 7 on two six-sided dice). This tool uses a seeded pseudo-random generator, so the same settings and seed reproduce the same sequence. Change the seed for another sequence. It is not cryptographic randomness.
Worked example
calculated with the default values below
Number of dice 2 · Sides per die 6 · Flat modifier 0 · Seed (same seed reproduces the same rolls) 7 Individual rolls 1, 1 · Total 2 · Total with modifier 2 · Expected average per roll 3.50 · Highest roll 1 · Lowest roll 1
Disclaimer
These calculators give general estimates for information and entertainment. Platform algorithms, metrics and definitions change without notice, and none of these results are official figures from the platforms named.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
r_i = int(u_i × s) + 1 → T = Σ r_i, T_m = T + m, μ = (s + 1) ÷ 2
- n
- number of dice
- s
- sides per die
- m
- flat modifier
- r_i
- individual roll
- μ
- expected average per die
The u_i stream comes from a seeded PRNG and the loop stops after n rolls. μ is the theoretical mean of one die, independent of the actual rolls; highest and lowest are the extrema of this batch.
Frequently asked questions
Why is the expected average exactly one above half the sides?
The tool reports the expected average per roll as (sides + 1) / 2, because a fair die from 1 to N is uniformly distributed and its mean is the midpoint. For the default 2d6 the per-roll expectation is 3.5, so an unmodified total of two dice centres on 7, while the flat modifier you add simply shifts the whole distribution. The seeded generator gives the actual individual rolls, highest and lowest, but those vary around this fixed average rather than changing it.