Dice Roller

Roll any standard dice — d4, d6, d8, d10, d12, d20, d100 — or enter a custom NdX+modifier expression. Perfect for tabletop RPGs, board games, and probability experiments.

Quick Roll

Custom Roll e.g. 2d6+3, 1d20, 3d8-1

What is a Dice Roller?

A dice roller is a random number generator that simulates the outcomes of rolling physical polyhedral dice — the six-sided die (d6) being the most familiar, alongside the four-sided (d4), eight-sided (d8), ten-sided (d10), twelve-sided (d12), twenty-sided (d20), and percentile (d100) dice used in tabletop role-playing games. Digital dice rollers use pseudorandom number generation (typically JavaScript's Math.random()) to produce outcomes that simulate the uniform probability distribution of a fair physical die.

Standard dice notation — the format NdX±M — compactly encodes roll instructions: N is the number of dice, X is the number of sides per die, and the optional modifier ±M is added to or subtracted from the total sum. For example, 2d6+3 means "roll two six-sided dice and add 3," producing results from 5 to 15. This notation, widely used in Dungeons & Dragons and other tabletop RPGs, board games, and wargames, expresses complex probability distributions concisely and unambiguously.

The statistical properties of dice rolls follow well-defined probability distributions. A single die roll is uniformly distributed (each face equally probable). Multiple dice summed together produce a bell-curve distribution through the Central Limit Theorem — rolling 2d6 gives values from 2 to 12, with 7 as the most probable result (6 of 36 combinations = 16.7%). Rolling with advantage in D&D (keeping the higher of two d20 rolls) raises the expected value from 10.5 to approximately 13.8, while disadvantage lowers it to approximately 7.2.

Dice Notation Guide

Standard dice notation uses the format NdX+M where N is the number of dice, X is the number of sides, and M is an optional modifier.

1d6

One six-sided die

2d6+3

Two d6 plus 3

1d20

D20 (attack roll)

4d6

Four d6 (ability score)

1d100

Percentile

3d8-2

Three d8 minus 2

How the Dice Roller Works

Formula, assumptions, and calculation steps for this dev tools tool.

Formula Used

Uses a pseudo-random number generator to produce a uniform result between 1 and the number of sides

Methodology

Generates a uniformly distributed pseudo-random integer between 1 and the selected number of die sides.

Calculation Steps

Provide the input text or select generation options.
Apply the selected encoding, parsing, hashing, or formatting rule.
Validate the output where possible.
Return copy-ready developer output.

Assumptions and Limits

Generated or transformed output depends exactly on the supplied input.
Security-sensitive values should be handled carefully.
Browser tools do not replace production validation.

Frequently Asked Questions

What is a d20 used for in D&D?

The d20 (20-sided die) is the core die in Dungeons & Dragons. It is rolled for attack rolls, ability checks, and saving throws. You roll d20 + your relevant modifier against a target number (DC or AC). A natural 20 is a critical hit; a natural 1 is a critical fail.

How do I roll ability scores in D&D 5e?

The standard method is to roll 4d6 and drop the lowest die, repeating six times for the six ability scores (Strength, Dexterity, Constitution, Intelligence, Wisdom, Charisma). The average result is about 12.2 per score. Some groups use point-buy or the standard array (15, 14, 13, 12, 10, 8) instead.

What is a percentile dice (d100)?

A d100 (or percentile die) gives a result from 1 to 100. Traditionally it is rolled as two d10s — one representing tens (00–90) and one representing units (0–9). A result of 00 and 0 is usually read as 100. It is used for percentage-based skill checks and random tables.

What does rolling with advantage mean?

Rolling with advantage means you roll two d20s and take the higher result. Disadvantage is the opposite — roll two d20s and take the lower. Mathematically, advantage raises the average d20 roll from 10.5 to about 13.8, and disadvantage lowers it to about 7.2.

Real-World Applications

🐉

Tabletop RPGs

Roll attack, saving throw, and skill check dice for D&D, Pathfinder, and other TTRPGs.

🎲

Board Games

Replace physical dice for travel-friendly gaming or when dice go missing mid-session.

🎓

Probability Education

Run statistical experiments — roll 100 d6s to demonstrate the law of large numbers in class.

🎮

Game Design Prototyping

Test mechanical outcomes for a dice system before investing in physical production.

🏆

Tournament Tie-Breaking

Use a fair virtual roll to break ties without a physical die in online tournaments.

📊

Monte Carlo Simulations

Use dice rolls as a classroom analogy for random variable generation in statistics.

Common Mistakes

Misreading "advantage/disadvantage" mechanics

Advantage in D&D means roll two d20s and take the higher — it's not a modifier; the system only uses the die-selection approach.

Expecting uniform distribution from small samples

Rolling a d6 ten times rarely produces each face exactly once — variance is normal and expected in small trials.

Confusing dice notation order

In XdY+Z, X is the number of dice, Y is sides per die, and Z is a flat modifier — 2d6+3 ≠ 2d(6+3).

Assuming pseudorandom is "less fair"

Cryptographically secure PRNGs used in quality dice rollers are statistically indistinguishable from true randomness.

Forgetting the +1 modifier on minimum values

A d6 produces values 1–6, not 0–5. Always verify the minimum result is 1, not 0, for game mechanics.

Polyhedral Dice Quick Reference

Die	Faces	Mean Roll	Common Use
d4	4	2.5	Dagger damage, cantrip
d6	6	3.5	Standard damage, board games
d8	8	4.5	Longsword, healing word
d10	10	5.5	Crossbow, percentile half
d12	12	6.5	Greataxe, bardic inspiration
d20	20	10.5	Attack rolls, saving throws
d100	100 (2×d10)	50.5	Percentile tables

References

Gygax, Gary & Arneson, Dave. Dungeons & Dragons. TSR, 1974.
Crawford, Jeremy et al. Dungeons & Dragons Player's Handbook (5th ed.). Wizards of the Coast, 2014.
Weiss, Eric. "Polyhedral Dice Design." Games & Puzzles, 1975.
DeGroot, Morris H. & Schervish, Mark J. Probability and Statistics. Pearson, 2012.
Peterson, Jon. Playing at the World. Unreason Press, 2012.