123DiceRoller
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Dice Range Roller

Type the lowest and highest total you want. The roller picks the fewest real dice that cover exactly that range, puts them on the table and shows the odds of every total.

Setting up the table…

Tap the table to roll · tap a die to hold it

Ready to roll

Press Roll, tap the table, or press R.

Number range to
Modifier −2

Type a roll like 3d6+2, 4d6dl1 or d20 adv. Notation guide

Quick roll

The chance of every total appears here.

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Full probability table

How to use it

Type the lowest and the highest total you want in the two boxes above the dice. The roller works out the dice, sets them in the picker with the modifier, and shows the odds of every total in the Probability panel. Press Roll, tap the table or press R to throw them. The same two boxes, under “Number range”, are in the custom roll on every other roller on this site.

How the dice are chosen

A die adds at least 1 and at most its number of sides to a total, so each die widens the range by its sides minus one: a d6 by 5, a d20 by 19, a d100 by 99. To cover a range, the roller finds dice whose widths add up to the gap between your two numbers, then adds or subtracts a modifier so that the lowest possible total lands on your lower limit.

Take 1 to 50. The gap is 49, and 19 + 19 + 11 = 49, so two d20s and a d12 fit. On their own they roll 3 to 52; taking away 2 makes it exactly 1 to 50, which is 1d12+2d20-2. The roller always uses the fewest dice that fit, then the fewest different sizes, so 2 to 12 is the familiar 2d6 rather than a d4 and a d8.

The dice for some common ranges
RangeDiceChance of the lowest total
1–61d61 in 6
5–101d6+41 in 6
2–122d61 in 36
3–183d61 in 216
0–91d10-11 in 10
1–201d201 in 20
1–302d10+1d12-21 in 1,200
1–501d12+2d20-21 in 4,800
1–1001d1001 in 100

Why middle totals come up more often

A single die is flat: every face has the same chance. As soon as two or more dice are added together, a total in the middle can be made in more ways than one at either end. On 3d6 a 3 needs three 1s, one way out of 216, while a 10 can be made 27 ways, so a 10 or an 11 is 27 times as likely as a 3 or an 18. The chart in the Probability panel shows the exact curve for your range.

That shape is often what a game wants: ordinary results common, extreme ones rare. When a range needs only one die (4, 6, 8, 10, 12, 20 or 100 numbers, such as 1 to 20 or 5 to 10) every number is equally likely.

Ranges real dice cannot make

Each die widens a range by an odd number of at least 3, so no mix of dice covers exactly 2, 3 or 5 numbers. For those the roller uses a flat d2, d3 or d5, drawn on screen rather than thrown in 3D. At the table you can get them from ordinary dice:

  • 2 numbers, like a coin: roll any die, and read odd as 1 and even as 2.
  • 3 numbers: roll a d6 and halve it, rounding up, so 1–2 is 1, 3–4 is 2 and 5–6 is 3.
  • 5 numbers: roll a d10 and halve it, rounding up.

When every number must be equally likely

For a fair pick, like a raffle ticket or a random page, a sum of dice is the wrong tool, because the middle numbers win too often. Type 1d50 in the notation box instead: the roller draws a flat 50-sided die on which every number has a 2% chance. With real dice, roll a d100 and halve it, rounding up, and each number from 1 to 50 comes from exactly two results. When the count of numbers does not go into 100 evenly, re-roll the leftovers: for 1 to 30, roll a d100 and re-roll 91 to 100, then take 30 or 60 off anything above 30.

Frequently asked questions

What dice do I roll for a number from 1 to 50?

Two d20s and a d12, minus 2 (1d12+2d20-2). On their own they roll 3 to 52, and taking 2 away makes it exactly 1 to 50. Numbers near the middle come up more often than 1 or 50; for equal chances, type 1d50 in the notation box.

How do you make a range of numbers with dice?

Each die adds between 1 and its number of sides, so it widens the range by its sides minus one. Pick dice whose widths add up to the gap between your highest and lowest number, then add or subtract a modifier so the lowest total matches your lowest number. The roller does this for you with the fewest dice.

Why does the roller pick 3d6 for 3 to 18, not a 16-sided die?

It only uses dice you can throw on the table: d4, d6, d8, d10, d12, d20 and d100. Three d6s cover 3 to 18 exactly, with 10 and 11 the most common totals. If every number should be equally likely, type 1d16+2 in the notation box.

Can every number in a range be equally likely?

Only with a single die. Ranges of 4, 6, 8, 10, 12, 20 or 100 numbers get one die and equal chances. For any other size, type a single die and a modifier in the notation box, such as 1d50 or 1d30+10; it is drawn as a flat die.

What is the largest range the roller can make?

It can use up to 100 dice, so the widest range is 100 d100s: 9,901 numbers. The lowest and highest totals can be anywhere from −100,000 to 100,000.

More dice rollers

D4 4 sides D6 6 sides D8 8 sides D10 10 sides D12 12 sides D20 20 sides D100 Percentile
Dice Roller Roll any mix of 3D dice in your browser. Every result is drawn by a cryptographically secure random generator, then thrown across the table with real physics so you can watch it land. Roll a Die Tap Roll to throw one fair six-sided die. Each number from 1 to 6 has exactly the same 1-in-6 chance, every time. Roll 2 Dice Throw a pair of six-sided dice. Seven is the most common total (1 in 6); 2 and 12 are the rarest (1 in 36 each). D&D Dice Roller The full Dungeons & Dragons set — d4, d6, d8, d10, d12, d20 and d100 — with advantage, disadvantage, crits and a one-click ability-score roller. Yahtzee Dice Roller Five dice, three rolls a turn. Tap any die to hold it, roll the rest, and the roller tells you which scoring combinations you have. Dice Probability Calculator Type any roll — 3d6, 2d20kh1, 1d20+1d4+5 — to see the exact chance of every total, the average, and the odds of reaching a target. Dice Notation, Explained Dice notation writes a roll as NdS: N dice with S sides. 3d6+2 means roll three six-sided dice, add them up, then add 2.

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