Dice Roller
Roll any dice notation, with modifiers and totals.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- Notation
- 3d6+2
- This roll
- 1 + 1 + 4 + 2 = 8
- Average result
- 12.5
- Minimum / maximum
- 5 / 20
- Chance of maximum
- 0.463%
Quick answer
A fair die with d sides averages (d + 1) ÷ 2, so a d6 averages 3.5 and a d20 averages 10.5. For several dice, multiply by the number of dice and add any modifier: 3d6+2 averages 3 × 3.5 + 2 = 12.5, with a range of 5 to 20. The chance of rolling the maximum on n dice is 1 ÷ dⁿ, or 1 in 216 for 3d6.
What the Dice Roller does
Set the number of dice, the sides per die and a modifier, and the roller produces a fresh random roll showing each die, written in standard tabletop notation such as 3d6+2. It also gives the long-run average, the lowest and highest possible totals and the probability of hitting the maximum.
It works for any die size, not only the d4, d6, d8, d10, d12 and d20 of a typical tabletop set: a d100 for percentile rolls, a d3 or d7 for homebrew rules, or a 2d6 for board games. Rolls use the browser's pseudo-random number generator, which is uniform and unbiased for games but not intended for gambling or cryptography. For unrelated random picks, the random number generator gives a single number in any range.
The statistics assume fair dice. Physical dice can carry small manufacturing biases, especially cheap dice with drilled pips or uneven resin.
The formula
Average = n × (d + 1) ÷ 2 + m Minimum = n + m Maximum = n × d + m P(maximum) = 1 ÷ dⁿ
| Symbol | Meaning | Unit |
|---|---|---|
| n | Number of dice rolled | dice |
| d | Sides on each die | sides |
| m | Flat modifier added to (or subtracted from) the total | — |
These follow from basic probability for independent, uniformly distributed outcomes, as covered in any introductory probability text. The average of a single die is the mean of 1 to d. Totals of several dice cluster around the average in a bell shape because there are more combinations that make middle values. This page also replaces the former dice probability calculator; the tables below give exact probabilities for the most common rolls, and the probability calculator handles other combined events.
Worked examples
Attack roll with a +5 bonus
A tabletop RPG character rolls 1d20 and adds 5 to hit.
Inputs
- Number of dice1
- Sides per die20
- Modifier5
Result
- Notation1d20+5
- This roll8 + 5 = 13
- Average result15.5
- Minimum / maximum6 / 25
- Chance of maximum5%
Every total from 6 to 25 is equally likely at 5% each. Against an armor class of 15 you need a 10 or higher on the die, which is 11 faces out of 20, or a 55% chance.
Two-handed weapon damage
A greatsword hit dealing 2d6 plus a +3 strength bonus.
Inputs
- Number of dice2
- Sides per die6
- Modifier3
Result
- Notation2d6+3
- This roll2 + 3 + 3 = 8
- Average result10
- Minimum / maximum5 / 15
- Chance of maximum2.7778%
Damage averages 10 and ranges from 5 to 15. Because 2d6 peaks at 7, results of 9 to 11 are far more common than the extremes.
Small die with a fixed bonus
A spell dealing 1d4+1 damage.
Inputs
- Number of dice1
- Sides per die4
- Modifier1
Result
- Notation1d4+1
- This roll2 + 1 = 3
- Average result3.5
- Minimum / maximum2 / 5
- Chance of maximum25%
Averaging 3.5 with a range of only 2 to 5, it is a reliable rather than swingy effect. A fixed bonus raises the average without changing the spread.
Probability of each total with 2d6
There are 36 equally likely combinations of two six-sided dice. Seven is the most common total because six combinations make it, which is why it matters in games such as Monopoly, Catan and craps.
| Total | Combinations | Probability |
|---|---|---|
| 2 or 12 | 1 each | 2.78% each |
| 3 or 11 | 2 each | 5.56% each |
| 4 or 10 | 3 each | 8.33% each |
| 5 or 9 | 4 each | 11.11% each |
| 6 or 8 | 5 each | 13.89% each |
| 7 | 6 | 16.67% |
Averages and ranges of common rolls
Useful for comparing weapons, spells or house rules at a glance.
| Roll | Average | Range | Chance of maximum |
|---|---|---|---|
| 1d4 | 2.5 | 1–4 | 25% |
| 1d6 | 3.5 | 1–6 | 16.7% |
| 1d8 | 4.5 | 1–8 | 12.5% |
| 1d12 | 6.5 | 1–12 | 8.3% |
| 1d20 | 10.5 | 1–20 | 5% |
| 3d6 | 10.5 | 3–18 | 0.46% (1 in 216) |
| 8d6 | 28 | 8–48 | 1 in 1,679,616 |
Advantage, disadvantage and "at least one" rolls
- Advantage (roll 2d20, keep the higher): the average rises from 10.5 to about 13.8, and the chance of a natural 20 nearly doubles to 9.75%.
- Disadvantage (keep the lower): the average falls to about 7.2.
- At least one six: the chance of at least one 6 on n dice is 1 − (5/6)ⁿ. With 4 dice it is about 51.8%, just better than even.
- Rolling 4d6 and dropping the lowest (a common ability-score method) averages about 12.2, compared with 10.5 for straight 3d6.
How to use the Dice Roller
- 1Enter how many dice to roll (the X in XdY).
- 2Enter the sides per die (the Y): 4, 6, 8, 10, 12, 20, 100 or any other number.
- 3Enter a modifier to add, or a negative number to subtract; leave 0 for none.
- 4Read this roll's dice and total, and compare it with the average and range; recalculate for a new roll.
Frequently asked questions
What is the average roll of 3d6?
10.5. Each d6 averages 3.5, and three of them average 3 × 3.5. Totals of 10 and 11 are the most likely, each with a 12.5% chance.
What does 2d6+3 mean?
Roll two six-sided dice, add them together, then add 3. The result ranges from 5 to 15 and averages 10.
What are the odds of rolling a natural 20?
5%, or 1 in 20, on a single d20. With advantage (two dice, keep the higher) it rises to 9.75%.
Is an online dice roller truly random?
It uses a pseudo-random generator that produces evenly distributed results, which is fair for games. It is not suitable for gambling or security purposes.
What is the most common roll with two dice?
Seven, with a probability of 6 in 36, or 16.67%. Two and twelve are the least common at 1 in 36 each.
References
- Introduction to Probability, Blitzstein and Hwang — CRC Press
- Dungeons & Dragons Player's Handbook (dice notation and advantage rules) — Wizards of the Coast
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
- Report an error