D20 Dice Roller
Roll one or more twenty-sided dice, add a flat modifier, and choose normal, advantage, or disadvantage mode. The calculator shows your roll result, total with modifier, probability of meeting a target number, and the expected value for each mode. Every result updates the instant you click Roll.
Formula
Worked example
You roll a Perception check (DC 15) with a +4 modifier and advantage. You need the die to show at least 11 (15 - 4 = 11). With advantage, the probability is 1 - (10/20)^2 = 1 - 0.25 = 75%. Without advantage it would be 10/20 = 50%. The expected face value with advantage is about 13.8, so your expected total is 13.8 + 4 = 17.8.
How a d20 works
A d20 is an icosahedron - a regular twenty-sided solid - where each face is an equilateral triangle numbered 1 through 20. Because all faces are geometrically identical, each number has an equal probability of 1/20 = 5%. The expected (mean) value of a single roll is (1 + 20) / 2 = 10.5. In tabletop role-playing games like Dungeons and Dragons, the d20 is the primary resolution mechanic: you roll the die, add your character's relevant modifier, and compare the total to a Difficulty Class (DC) or an opponent's Armor Class (AC). Rolling a 20 before the modifier is a natural 20, often treated as an automatic or critical success, and rolling a 1 is a natural 1, often an automatic failure.
Advantage and disadvantage
Advantage and disadvantage are the two most impactful situational modifiers in D&D 5th edition. When you roll with advantage, you roll two d20s and keep the higher result. When you roll with disadvantage, you roll two d20s and keep the lower. Advantage raises your expected roll from 10.5 to approximately 13.83, effectively a +3.33 bonus. Disadvantage lowers it to roughly 7.17, effectively a -3.33 penalty. The benefit of advantage is largest when the DC is around 11 (a 50% base chance), where it pushes your probability from 50% to 75%. Near the extremes - a DC of 2 or DC 19 - its impact narrows. Multiple sources of advantage do not stack: two conditions granting advantage still result in rolling only two dice.
Reading probability and the difficulty class
The Difficulty Class (DC) is the number your total must meet or beat for success. With no modifier and a normal roll, the probability of success is simply (21 - DC) / 20. With a +5 modifier, a DC 15 check requires a roll of only 10, giving a 55% chance. Understanding probability helps you make tactical decisions: spending a resource to gain advantage is worth roughly 4 points of expected bonus, so if your modifier is already high enough that you succeed on a 4 or better, advantage offers little marginal value but protecting against fumbles is harder since natural 1s are automatic failures in many rulesets.
Rolling multiple d20s
Some spells and effects call for rolling more than one d20 simultaneously - for example, the Eldritch Blast cantrip can launch multiple beams, each requiring its own attack roll. When you roll multiple independent dice and sum them, the distribution shifts from flat (uniform) to a bell-curve shape centred on n * 10.5. Two d20s sum to an average of 21, three to 31.5. The bell-curve effect means extreme results (very high or very low sums) become less likely, reducing variance. This calculator supports up to 10 dice in normal mode.
D20 roll probability table
| Roll needed | Normal | Advantage | Disadvantage |
|---|---|---|---|
| 1 | 100% | 100% | 100% |
| 2 | 95% | 99.75% | 90.25% |
| 5 | 80% | 96% | 64% |
| 10 | 55% | 79.75% | 30.25% |
| 11 | 50% | 75% | 25% |
| 13 | 40% | 64% | 16% |
| 15 | 30% | 51% | 9% |
| 17 | 20% | 36% | 4% |
| 18 | 15% | 27.75% | 2.25% |
| 20 | 5% | 9.75% | 0.25% |
Chance of rolling at or above each value for normal, advantage, and disadvantage.
Frequently asked questions
What is the probability of rolling a natural 20?
With a single normal d20 roll the chance is exactly 1/20 = 5%. With advantage (roll two, keep highest) the probability of at least one natural 20 is 1 - (19/20)^2 = 1 - 0.9025 = 9.75%. With disadvantage (roll two, keep lowest) both dice must show 20, so the chance is (1/20)^2 = 0.25%.
Does advantage stack with itself?
No. In D&D 5e, no matter how many sources of advantage you have, you still roll only two d20s and keep the higher. The same applies to disadvantage. If you have both advantage and disadvantage from different sources at the same time, they cancel out and you roll a single d20 normally.
How much is advantage worth in flat modifier terms?
On average, advantage is worth about +3.3 to +4 modifier points, depending on where you start. It is worth most when your base success chance is near 50% and worth least when you already succeed or fail almost all the time. At a 50% base chance, advantage pushes you to 75% - a gain of 25 percentage points. Disadvantage is a symmetric penalty of about -3.3 to -4 expected modifier points.
What does the modifier represent in D&D?
In D&D 5e a modifier is a flat number added to the d20 result before comparing to the DC. It typically combines an ability score modifier (from your Strength, Dexterity, or other relevant stat) and possibly your proficiency bonus if you are trained in the skill or weapon. For example, a Strength modifier of +3 and proficiency bonus of +4 gives +7 on Strength-based weapon attack rolls.
What is the expected value of a d20 roll?
A single normal d20 has an expected value of 10.5, the average of all integers from 1 to 20. With advantage the expected value rises to approximately 13.83. With disadvantage it falls to approximately 7.17. These values assume a fair, unbiased die where each face has exactly a 5% probability.
How do I calculate the probability of meeting a DC?
For a normal single d20 roll: probability = (21 - (DC - modifier)) / 20, clamped to 0-100%. For advantage: probability = 1 - ((DC - modifier - 1) / 20)^2. For disadvantage: probability = ((21 - (DC - modifier)) / 20)^2. In all cases values below 1 and above 20 are clamped to 0% and 100% respectively.
What is the difference between a d20 roll and a percentile (d100) roll?
A d20 generates integers from 1 to 20 with equal probability, giving 5% increments. A percentile roll (two d10s read as tens and units) generates 1 to 100 in 1% increments and is used for finer probability checks such as wild magic surges. The d20 is the primary action resolution die in most tabletop RPGs, while the d100 appears for random tables and special mechanics.