Roll a d20: online 20-sided dice roller

How to use this d20 roller

Choose how many d20s you want to roll and, if your roll has a bonus or a penalty, set the modifier with + or −. Then press Roll, or pick the dice up with your finger or mouse, drag them and let go over the tray: they tumble with real physics and come to rest on their own.

Once they stop, the page reads the top face of each die. A 20 is flagged as a natural 20 (critical) and a 1 as a natural 1 (critical fail). The modifier is added to the result, so you see both the number on the die and the total. That matters because in almost every roleplaying game a critical or a fumble depends on the number the die shows, and the modifier plays no part in it.

The icosahedron: shape and numbering of the d20

A d20 is a regular icosahedron: 20 identical equilateral triangles as faces, 30 edges and 12 vertices, with five faces meeting at each vertex. It is one of the five Platonic solids, alongside the tetrahedron (d4), the cube (d6), the octahedron (d8) and the dodecahedron (d12). Plato, in the Timaeus, linked it with the element of water.

A die is fair when no face has an edge over the others. On a regular icosahedron every face is the same shape and the same distance from the centre, and any face can be rotated into the position of any other. On a well-made die each number therefore comes up with a probability of 1 in 20, or 5%. The d10 used in roleplaying games is not a Platonic solid (it is a pentagonal trapezohedron), but it is still fair because all its faces are identical.

Why opposite faces add up to 21

On a standard d20 the 20 sits opposite the 1, the 19 opposite the 2, the 18 opposite the 3, and so on down to 11 opposite 10. Each pair adds up to 21, just as opposite faces on a six-sided die add up to 7. The reason is practical: if a die comes out of the mould slightly flattened across two opposite faces, those two faces will turn up a little more often, but because they add up to 21 their average is still 10.5 and the flaw favours neither high nor low numbers.

Manufacturers also scatter high and low numbers across the whole surface so that they do not cluster in one area. Some "numerically balanced" d20s go further: they keep the pairs that add up to 21 and also make the five faces around every vertex add up to almost the same total, 52 or 53, since the exact average is 52.5.

A short history of the 20-sided die

Twenty-sided dice are more than two thousand years old. The Metropolitan Museum of Art in New York holds several icosahedra from Egypt with Greek letters on their faces, dated between the 2nd century BC and the 4th century AD; one is made of faience and another of serpentinite. The Louvre also has examples from the Ptolemaic and Roman periods. Most often each face carries a number written in Greek or Latin.

Nobody knows for certain what they were used for. The Met itself notes that nothing specific about their use has survived. One of its dice bears Greek words that resemble the names of throws in the game of knucklebones (astragals), which has led to the suggestion that they were used for games.

From wargames to Dungeons & Dragons

For much of the 20th century, dice with anything other than six sides were hard to come by. In the early 1970s, miniature wargamers wanted to model combat with finer odds than a d6 could offer, and used chits, home-made spinners or packs of cards. In 1972 an American educational supplies company released a set of dice based on the five Platonic solids, and gamers took it up.

In 1974 Gary Gygax and Dave Arneson turned their home-made rules into Dungeons & Dragons, which relied on those polyhedral dice, although they had to be bought separately. The early d20s were cheaply made and each face only had room for one digit, so they were numbered 0 to 9 twice. Players coloured one set of numbers to tell 1 to 10 from 11 to 20, and the same die doubled as a d10, which was not yet common. The publisher's first boxed sets with dice included that double-numbered d20; by the early 1980s the sets came with a d20 numbered 1 to 20 and a crayon to fill in the moulded numbers.

In 2000, with the third edition of D&D, Wizards of the Coast put the d20 at the heart of the whole rulebook: attacks, saves and checks are all resolved by rolling a d20, adding modifiers and comparing the total with a target number. It released that rules core as the "d20 System" under an open licence and also used it for other games, such as the Star Wars Roleplaying Game (2000) and d20 Modern (2002). Many other publishers adopted it, which is why "d20" is now almost shorthand for tabletop roleplaying.

d20 rules in D&D 5th edition and other RPGs

In the fifth edition of Dungeons & Dragons nearly everything that can go right or wrong is settled with a d20. The 2024 revised rules call these rolls D20 Tests and split them into three kinds:

If the total equals or beats the target number, the roll succeeds. These are the typical difficulties given in the basic rules:

Natural 20s and natural 1s

Under the fifth edition basic rules, a natural 20 and a natural 1 only have an automatic effect on attack rolls. A 20 on the die always hits, whatever the target's AC, and it is a critical hit: you roll all of the attack's damage dice twice and then add the usual modifiers. A 1 on the die always misses. For ability checks and ordinary saving throws the rules give no automatic success or failure for rolling a 20 or a 1. Plenty of tables play it that way as a house rule, so it is worth agreeing before the session starts.

Death saving throws

A character who starts their turn on 0 hit points rolls 1d20: 10 or higher counts as a success and anything lower as a failure. Three successes and the character is stable; three failures and they die. Here the die really does decide things: a natural 20 means the character regains 1 hit point, and a natural 1 counts as two failures.

Advantage and disadvantage

With advantage you roll two d20s and use the higher; with disadvantage, the lower. Several sources of advantage do not stack, so you never roll more than two dice, and if a roll has both advantage and disadvantage they cancel out and you roll a single die. Passive checks involve no roll at all: they are 10 plus your modifiers, with +5 for advantage and −5 for disadvantage. That +5 matches what advantage is worth on rolls of medium difficulty, as the probability table shows.

Other games that use the d20

In Pathfinder (second edition) a natural 20 improves the result by one degree (a failure becomes a success, a success becomes a critical success) and a natural 1 makes it one degree worse. Beating the DC by 10 or more is also a critical success, and missing it by 10 or more is a critical failure. Magic: The Gathering has cards that tell you to roll a d20 too, and many board games use one to resolve tables of random events.

d20 probabilities, with advantage and disadvantage

On a well-made d20 each number has a 5% chance of coming up and the average roll is 10.5. The chance of rolling X or higher is (21 − X) / 20: an 11 or higher comes up half the time, and each point of modifier shifts that chance by 5 percentage points. With advantage the chance is 1 − (1 − p)², and with disadvantage it is p², where p is the chance with a single die.

The table shows the chance of rolling the given number or higher on the die, before modifiers. To use it with a modifier, subtract the modifier from the DC: with +4 against DC 15 you need an 11 or higher on the die, which is 50% with one die, 75% with advantage and 25% with disadvantage.

• The average with advantage is 13.825 and with disadvantage 7.175, compared with 10.5 for a single die.
• Advantage helps most when you need a middling number: for 11 or higher it takes you from 50% to 75%, the same as a +5. For a natural 20 it only lifts the chance from 5% to 9.75%.
• With disadvantage a natural 20 has a 0.25% chance (1 in 400), and the chance of a natural 1 rises from 5% to 9.75%.

Rolling several d20s at once

Roll several dice and the chance of seeing at least one 20 climbs quickly. Each die is independent: three natural 1s in a row change nothing about the next roll.

The spindown d20 from Magic: The Gathering

In Magic: The Gathering each player starts on 20 life in the standard formats, and many keep track with a d20 known as a spindown. Its numbering is different from a roleplaying d20: the numbers run in order, each one next to the following one, so going from 14 to 13 just means turning the die to the neighbouring face. Wizards of the Coast has included spindowns in a number of its products, often with the set symbol on the 20 face.

That ordering is exactly what makes it a poor die for rolling. With similar numbers grouped together, the result is easier to influence. The Magic Tournament Rules do not allow a spindown to be used when a card asks you to roll a die, and in 2021, when Adventures in the Forgotten Realms brought in cards that say "roll a d20", Wizards confirmed that any method is fine as long as every result is equally likely. Those rules do not apply to casual games, but if you want a clean roll, use a d20 with standard numbering, like the one on this page.

Loaded and unbalanced dice: the salt water test

A cheap plastic d20 can have air bubbles or denser patches inside, and a handmade resin die can end up with its centre of gravity off-centre. Either way the heavier side tends to settle at the bottom and the opposite number comes up more than it should. A deliberately loaded die does the same with a hidden weight.

The salt water test is a simple way to spot that kind of internal imbalance:

1. Fill a glass with warm water and dissolve salt in it until the die floats. If it sinks, add more salt. Epsom salt (magnesium sulphate) dissolves more easily and gives you a stronger solution.
2. Drop the die in and flick it so it spins.
3. When it settles, note which number is on top. Repeat several times.
4. If the number keeps changing, there is no concentrated weight. If the same number, or two or three neighbouring ones, keeps turning up, the die has a heavy side, opposite those numbers.

The test has its limits. It only shows how the weight is distributed, not shape faults such as uneven faces or badly finished edges. Metal dice and many resin ones are too dense to float. And water is nothing like a real roll. For a proper check you need a rolling test: roll the die several hundred times, record the results and use a statistical test such as chi-squared to see whether the spread is further from even than chance would explain. With 20 faces, just getting 25 expected results per face takes 500 rolls.

Practical tips for rolling a d20