Roll 1d20
A twenty-sided die is an icosahedron, twenty identical triangles, and it is the die people picture when someone says role-playing game. Every face has the same chance, which makes the roll dramatic and unpredictable in equal measure. Modifiers do all the work of making a character good at something.
Press Roll to throw the dice.
Press Space to roll again. Type notation like 2d6+3 or 4d6dl1 straight into the box.
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Rolling 1d20 gives a result from 1 to 20, and on a fair die each one is equally likely at 5%. There is no curve and no typical result to plan around. The average sits at 10.5, which is a number the die itself can never show.
- Minimum
- 1
- Maximum
- 20
- Mean
- 10.5
- Median
- 10.5
- Std deviation
- 5.77
- Chance per result
- 5%
1d20 probability distribution
One die means one way to make each result, so the chart is a flat line rather than a curve. Add a second die and the totals immediately start clustering.
| Total | Ways | Probability | This or lower |
|---|---|---|---|
| 1 | 1 | 5% | 5% |
| 2 | 1 | 5% | 10% |
| 3 | 1 | 5% | 15% |
| 4 | 1 | 5% | 20% |
| 5 | 1 | 5% | 25% |
| 6 | 1 | 5% | 30% |
| 7 | 1 | 5% | 35% |
| 8 | 1 | 5% | 40% |
| 9 | 1 | 5% | 45% |
| 10 | 1 | 5% | 50% |
| 11 | 1 | 5% | 55% |
| 12 | 1 | 5% | 60% |
| 13 | 1 | 5% | 65% |
| 14 | 1 | 5% | 70% |
| 15 | 1 | 5% | 75% |
| 16 | 1 | 5% | 80% |
| 17 | 1 | 5% | 85% |
| 18 | 1 | 5% | 90% |
| 19 | 1 | 5% | 95% |
| 20 | 1 | 5% | 100% |
When you'd roll 1d20
The d20 is the resolution die. You roll it, add your bonus, and compare against a difficulty number or an opponent's defence. Because the die is flat, a plus one is worth the same whether the task is easy or brutal, and a bad roll can sink an expert. That flatness is the reason a natural 20 feels like a lightning strike and a natural 1 gets its own groan at the table.
Where this roll shows up
- Attack rolls, saving throws and ability checks in D&D third edition onward and in Pathfinder
- The d20 System and the games published under the Open Game License
- Advantage and disadvantage in fifth edition, where you roll two and keep one
1d20 questions
What is a natural 20?
The die itself showing 20, before any bonuses are added. On an attack roll in fifth edition it always hits and the damage dice are doubled. Many tables also treat it as an automatic success on other rolls, though the rules do not actually say that.
How does advantage work?
You roll two d20s and use the higher one. Disadvantage does the reverse and uses the lower. It is a clean way to represent a favourable or awkward situation without adding another number to track, and it shifts your typical result noticeably.
Why is the d20 flat instead of a curve?
Because it is a single die, and a single fair die gives every face the same chance. Systems that want a curve roll several dice instead. The flat d20 trades predictability for drama, which suits a game where one roll can decide a fight.
Is a d20 fair?
A well made one is. All twenty faces are identical equilateral triangles, so nothing favours a particular result. Cheap dice can be slightly off from air bubbles or trimming, and serious players test suspect dice by floating them in salt water and spinning them.