Single die
Roll a d20
A 20-sided die, rolled in your browser. Every face has an equal 5.00% chance, which works out to 1 in 20.
The odds on a d20
A single die is flat: no total is more likely than any other. The curve only appears once you roll more than one, which is what the odds calculator is for.
- Lowest
- 1
- Highest
- 20
- Average
- 10.50
- Each face
- 5.00%
- Odds
- 1 in 20
Every bar the same height. That flatness is the whole point of a single die: 5.00% per face, no favourites.
What a d20 is for
The one that matters. Attack rolls, saving throws, ability checks, and every moment the table goes quiet.
Why everything hangs off this one
The icosahedron is flat: every face is 5%, which makes the arithmetic at the table trivial. A target number of 15 succeeds 30% of the time and you can work that out in your head. Any curved die would make the same question a lookup.
Flatness also means the d20 is maximally swingy, and that is the design choice, not an accident. A trained expert and a complete amateur are separated by a handful of points of modifier against a twenty point roll, so the amateur succeeds sometimes and the expert fails sometimes. Systems that dislike that outcome tend to replace the d20 with 3d6, which covers a similar span but clusters hard in the middle so competence wins far more reliably.
Advantage is the one mechanic that bends the flat line without abandoning it. Rolling two and keeping the higher is worth roughly +3.3 on average, but the bonus is not evenly distributed: it does almost nothing when you need a 2 or a 20 and peaks in the middle, near a target of 11, where it swings the odds by 25 points. The table above shows exactly how much it is worth at every target number.
Note that this is two dice keeping one, which is not the same as 2d20 added together.
Hitting a target number
What a flat d20 beats, and how much two-dice advantage moves it.
| Need | Flat | Advantage | Disadvantage |
|---|---|---|---|
| 2+ | 95.0% | 99.8% | 90.2% |
| 4+ | 85.0% | 97.8% | 72.2% |
| 6+ | 75.0% | 93.8% | 56.2% |
| 8+ | 65.0% | 87.8% | 42.2% |
| 10+ | 55.0% | 79.8% | 30.2% |
| 12+ | 45.0% | 69.8% | 20.2% |
| 14+ | 35.0% | 57.8% | 12.2% |
| 16+ | 25.0% | 43.8% | 6.25% |
| 18+ | 15.0% | 27.8% | 2.25% |
| 20+ | 5.00% | 9.75% | 0.250% |
How to use this roller
Tap the die or press the roll button. To roll several at once, change How many, and the chart above redraws to the distribution you are actually rolling. To add a bonus, put it in Modifier: entering 3 turns a d20 into 1d20+3. Negative numbers work for penalties. The keyboard shortcut is R. After a roll, Copy link gives you a URL that shows exactly that result to whoever opens it.
Nothing is stored on a server and no account is needed. The page works offline once loaded, which matters if the venue has poor signal.
Common questions about the d20
What are the odds of rolling a 20 on a d20?
The odds of rolling a 20 on a d20 are exactly 5.00%, or 1 in 20. Every face on a fair d20 is equally likely, so a 20 is no rarer than any other number.
What are the odds of rolling two natural 20s in a row?
The odds of two natural 20s in a row are 1 in 400, or 0.25%. Each roll is independent, so after one natural 20 the next roll is still exactly 5%. The die has no memory, and a hot streak does not make the next 20 any more or less likely.
How can you tell if a physical d20 is unbalanced?
The usual home test is to float the die in a glass of heavily salted water, flick it to spin a few dozen times, and note which face ends up on top. A balanced die shows no pattern. If the same few numbers keep surfacing, there is an air bubble or uneven resin on the opposite side. A roller like this one has no such problem: every face is exactly 5%.
Does rolling with advantage change the odds of a 20?
With advantage, the chance of rolling a 20 on a d20 rises from 5.00% to 9.75%, close to double. It helps most in the middle of the range: the odds of rolling 11 or better go from 50.0% to 75.0%.