Dice Notation Explained — Reading 3d6+2, 4d6kh3 and 2d20kh1
Open any roleplaying rulebook and you will hit something like 2d6+3 before the end of the first page. It looks like algebra and it puts people off, but it is one of the simplest notations in gaming — a compact way of writing “roll this many of that die and do this to the result.” Once you can read it you can read every rulebook, every character sheet, and every online dice roller’s input box.
The core: NdS
The basic form is NdS, where N is how many dice to roll and S is how many sides each one has.
1d6— roll one six-sided die. Result: 1 to 6.3d6— roll three six-sided dice and add them together. Result: 3 to 18.2d20— roll two twenty-sided dice. Result: 2 to 40, though as we will see, you usually do not add these.
The d is just the separator; it stands for “die” or “dice” and it is never capitalised in the middle of a roll, though you will see D6 used on its own when someone is naming the die rather than writing a roll.
If the count is missing, it is 1. d20 and 1d20 mean exactly the same thing, and rulebooks use both, sometimes in the same paragraph. Nobody is being inconsistent on purpose — it is just a convention loose enough that everyone reads through it.
Dice are added, not concatenated. This is the single most common beginner mistake. 2d6 is not a number from 11 to 66; it is the sum of two dice, from 2 to 12. And critically, the results are not spread evenly across that range — see why 2d6 is a bell curve.
Modifiers: the + and − on the end
A modifier is a flat number added to or subtracted from the total after all the dice are rolled.
1d8+3— roll a d8, add 3. Result: 4 to 11.2d6-1— roll two d6, add them, subtract 1. Result: 1 to 11.1d20+7— the shape of nearly every attack roll and skill check in fifth-edition DnD, where the 7 is your proficiency and ability bonus rolled into one number.
Two things about modifiers that catch people out:
The modifier applies once, not per die. 3d6+2 means roll three dice, total them, then add 2 — a range of 5 to 20. It does not mean add 2 to each die. If a rule genuinely wants a bonus on every die, it will write it that way in words, and you will notice, because that is a much bigger effect.
A modifier changes the floor and the ceiling equally. It shifts the whole distribution up or down without changing its shape. 1d20+5 is exactly as swingy as 1d20; it just lives five points higher. This is why bonuses in a d20 system feel less powerful than players expect — the die is still doing all the varying.
Multiple dice types in one roll
Rolls can chain terms together with + and −:
1d8+1d6+3— a longsword hit with a bit of fire damage and a modifier.2d6+1d4— two different dice, totalled.
Each term is resolved separately and the results are added. In practice you roll them all at once and add up the lot; the notation just records what is in the handful.
Keep and drop: kh, kl, dh, dl
This is the part of the notation that genuinely needs explaining, because it is where the notation stops describing a sum and starts describing a selection.
kh— keep highest.2d20kh1means roll two d20s and keep the single highest. That is advantage in DnD, written as a roll.kl— keep lowest.2d20kl1is disadvantage.dl— drop lowest.4d6dl1means roll four d6 and discard the worst one, keeping the other three. That is the classic DnD stat-rolling method.dh— drop highest. Rarer, but it exists in games that punish you for overreaching.
The number after the letters is how many dice to keep or drop, not which ones. 4d6kh3 and 4d6dl1 describe exactly the same roll from opposite directions: four dice, three of them counted. Both notations are in common use and different tools prefer different ones, which is why most rollers accept both.
Some systems write these differently. You will see 4d6b3 (best three), 4d6h3, or in older books just an English sentence: “roll 4d6 and discard the lowest die.” They all mean the same thing.
Other symbols you will meet
r, reroll. 1d6r1 means reroll any 1 and take the new result. Great Weapon Fighting in fifth edition is effectively Nd6r1r2 on the damage dice, though the rulebook writes it in prose.
!, exploding dice. In some systems, rolling the maximum on a die lets you roll it again and add. 1d6! on a 6 becomes 6 plus another d6, which can itself explode. Savage Worlds is built on this, and it gives small dice a very long tail.
dF, Fudge or Fate dice. Six-sided dice marked with two +, two − and two blanks. 4dF gives a result from −4 to +4 centred hard on zero.
d% or d100, percentile. Traditionally two d10s read as tens and units. See the d100 page for how the pairing works.
Reading a rulebook line in practice
Here is a fifth-edition spell entry, cut down: “On a hit, the target takes 3d6 piercing damage. At Higher Levels: the damage increases by 1d6 for each slot level above 1st.”
That reads as: 3d6 at first level, 4d6 at second, 5d6 at third, and so on. The notation tells you the shape of the increase — more dice, not a bigger die, so the spell gets more reliable as well as bigger. A spell that scaled by moving from 1d6 to 1d8 to 1d10 would grow its ceiling without ever becoming predictable. Designers choose between those deliberately.
And a character sheet line: Longsword +7, 1d8+4 slashing.
Two rolls, not one. First 1d20+7 against the target’s AC. If that hits, 1d8+4 for damage. The +7 and the +4 are different numbers because one includes proficiency and the other does not — a detail the notation does not explain but the rules do.
Typing notation into this roller
The notation box on the dice roller accepts the forms you will actually meet:
3d6+2— dice with a flat modifier4d6kh3or4d6dl1— keep or drop2d20kh1— advantage1d8+1d6+3— mixed diced20— the count is optional
It rolls each die with the same cryptographically secure random source used by the buttons, and shows every individual die alongside the total, so you can check the maths rather than trusting it.
A short reference
| Notation | Meaning | Range |
|---|---|---|
1d6 |
one six-sided die | 1–6 |
3d6 |
three d6, summed | 3–18 |
1d20+5 |
a d20 plus five | 6–25 |
2d6-1 |
two d6, minus one | 1–11 |
4d6kh3 |
four d6, keep the best three | 3–18 |
4d6dl1 |
the same roll, written as a drop | 3–18 |
2d20kh1 |
advantage | 1–20 |
2d20kl1 |
disadvantage | 1–20 |
1d8+1d6 |
two different dice, summed | 2–14 |
The notation is worth learning for one practical reason: it is the shortest way to say precisely what you mean. “Roll four six-siders and throw away the worst one” is nine words and still slightly ambiguous. 4d6dl1 is six characters and is not ambiguous at all.