D20 Dice Roller

The die that decides everything

If you only own one polyhedral die, it’s probably a d20. In Dungeons & Dragons and the many games built on its rules, the twenty-sider decides whether you hit, whether you resist the dragon’s breath, whether you spot the trap, and whether your character survives the night. Everything else just measures how much.

The rule underneath it is simple: roll a d20, add your modifier, and compare the total with a target number. Meet or beat it and you succeed. Because each face is 5%, every +1 bonus is worth five percentage points, and you can do the arithmetic in your head once you get used to it.

Advantage and disadvantage, in actual numbers

Fifth edition’s best design idea is advantage: when the odds are in your favour, roll two d20s and keep the higher. When they’re against you, roll two and keep the lower. Choose the mode in the roller and it shows both dice and highlights which one counts.

How much does it help? More than people think, especially in the middle of the range. Here’s the chance of rolling at least a given number:

Need to roll	Normal	Advantage	Disadvantage
5+	80%	96%	64%
8+	65%	87.8%	42.3%
10+	55%	79.8%	30.3%
12+	45%	69.8%	20.3%
15+	30%	51%	9%
18+	15%	27.8%	2.3%
20	5%	9.75%	0.25%

Look at the 10+ row. Advantage takes a coin flip and turns it into roughly four in five. That’s worth about +5 on a typical roll, which is why a lot of players describe advantage as “roughly plus five” at the middle of the range. At the extremes it’s worth much less; if you need a natural 20, advantage only gets you from 5% to 9.75%.

Disadvantage is brutal on hard rolls. Needing a 15 or higher with disadvantage is a 9% shot. If your character has disadvantage on something important, it’s usually worth spending a turn to remove it.

Averages

A single d20 averages 10.5. With advantage the average roll climbs to about 13.8; with disadvantage it falls to about 7.2. That’s a gap of more than six points between the two, from nothing more than circumstance.

Probabilities for one d20

Roll	Chance of exactly this	Chance of this or higher
1	5%	100%
2	5%	95%
3	5%	90%
4	5%	85%
5	5%	80%
6	5%	75%
7	5%	70%
8	5%	65%
9	5%	60%
10	5%	55%
11	5%	50%
12	5%	45%
13	5%	40%
14	5%	35%
15	5%	30%
16	5%	25%
17	5%	20%
18	5%	15%
19	5%	10%
20	5%	5%

Critical hits and fumbles

A natural 20 on an attack roll is a critical hit in fifth edition: it hits regardless of the target’s armour, and you roll the attack’s damage dice twice. A natural 1 is an automatic miss. On ability checks and saving throws, the official rules give the natural 20 no special power (except for death saves), though plenty of tables play it as an automatic success anyway. That’s a house rule, and it’s worth agreeing on before the session rather than mid-argument.

Over a long session of, say, 60 attack rolls, you’d expect about three natural 20s and three natural 1s. Going a whole evening without a crit is less unusual than it feels: the chance of zero 20s in 60 rolls is about 4.6%, which means it’ll happen to someone at a busy convention table most days.

Why a digital d20 can be fairer

Physical d20s are rounder than other dice, so they roll a long way, and cheap ones are often slightly imperfect. Players test them with the salt-water float: dissolve enough salt in a glass of water that the die floats, then spin it gently a few times. If the same number keeps floating to the top, the die has a heavy side. Plenty of budget dice show a clear bias in this test.

Software dice don’t have that problem. This roller draws each result from your browser’s cryptographic random source, with rejection sampling to make sure every face gets exactly one chance in twenty. It won’t feel “hot” or “cold”; streaks happen, but they’re the honest kind.

Rolling several d20s

Some situations call for more than two twenty-siders: a group stealth check, mass combat with a dozen goblins, or rolling initiative for a crowd of monsters. Set Dice to the number you need, keep Roll mode on Sum all dice, and read each die from the list. Ignore the total if you’re checking each one separately.

For the Bless spell, roll your d20 here and then add a d4 from the d4 roller. For damage after a hit, the d6, d8 and d12 pages cover most weapons. And if you just want a flat number from 1 to 20 for a class activity, the 1 to 20 generator has a wheel for that.

Picking a sensible target number

If you’re running a game, the d20 maths helps you set difficulty fairly. Fifth edition’s own guidelines describe a DC of 10 as easy, 15 as medium and 20 as hard. For a character with a +5 bonus, that’s an 80%, 55% and 30% chance of success respectively. Those numbers are worth knowing, because “medium” in the rules is closer to a coin flip than most new game masters expect.

A rule of thumb we use: if failure would stop the story dead, either don’t call for a roll or set the target low. Save the hard rolls for moments where failing is interesting.

The d20 outside of D&D

Twenty-sided dice turn up well beyond dungeon crawls. Pathfinder, Starfinder and a long list of other games use the same roll-plus-modifier system. Teachers use a d20 to pick one of twenty spelling words or students. Some quiz shows at pub nights use one to pick a category from a numbered list. Wherever you need twenty equal outcomes, it’s the obvious tool.