Dice Probability Calculator

How the dice probability calculator works

1. Set the pool. Enter how many dice you roll and how many sides each one has, or tap a d4, d6, d8, d10, d12, d20 or d100 preset to fill the sides in.
2. Choose how the dice are added up. Total of every die covers damage rolls and 2d6 checks. Keep the highest covers ability scores rolled as 4d6 keep highest 3 and every advantage-style roll. Keep the lowest covers disadvantage.
3. Add the modifier. A +5 attack bonus or a −2 penalty is applied after the dice are read, exactly as it is at the table.
4. Say what you need. Pick at least for a difficulty class or armour class, at most for a roll-under check, or exactly when a single total matters.
5. Read the odds and the spread. The headline is the chance of hitting your number; the table underneath shows the chance of every total, and the comparison table shows what the same target looks like rolled normally, with the best of the pool and with the worst.

Reading the results

Every probability here is exact, not sampled. The calculator counts the combinations behind each total and divides by the number of equally likely outcomes, so 2d6 rolling at least 9 is exactly 10 in 36, or 27.78%, and a single d20 hitting a target of 15 or better is exactly 6 in 20, or 30.00%. Nothing is estimated and nothing is left to chance, which is the point of using a calculator instead of rolling and hoping.

The average total is where the pool centres over many rolls, and thestandard deviation is how widely results scatter around it. Eight d6 average 28 with a standard deviation of 4.83, so a total of 28 is ordinary and a total of 45 is a story you will tell for years. The middle 80% line is often more useful than either: it is the band four rolls in five land inside, which is the honest answer to "what should I expect from this roll tonight".

The comparison table answers the question players actually argue about. Rolling the best of two d20 is not the same as adding +3, and the table shows both sides of it: with a +5 modifier against a target of 15, a normal roll succeeds 55.00% of the time, advantage succeeds 79.75% of the time and disadvantage succeeds only 30.25% of the time.

Worked example: advantage on a DC 15 check

Your character has a +5 bonus and needs to hit a difficulty class of 15, so the die itself has to show 10 or better. Roll one d20 and the chance is 11 faces out of 20, or 55.00%. Roll two d20 and keep the higher, and the only way to fail is for both dice to come up 9 or less: that is 9/20 times 9/20, so the chance of failure falls to 20.25% and the chance of success rises to79.75%. Roll with disadvantage and the same target succeeds only30.25% of the time, because now both dice have to come up 10 or better.

Set the pool to 2d20, keep the highest 1, add a +5 modifier and ask for at least 15 to reproduce those three numbers on this page.

Worked examples: damage pools and ability scores

An 8d6 fireball averages 28 damage, but the average is not the answer anyone needs at the table. The chance of rolling 28 or more is 54.05%, so a wizard is very slightly more likely than not to beat their own average, and the middle 80% of rolls sits between 22 and 34. Ask for at least 35 and the odds drop to a little under 8%, which is why high damage rolls feel memorable.

For ability scores, the classic 4d6 drop lowest is the same as keeping the highest 3 of 4d6. The average is 12.24, not the 14 you would get from a straight 4d6, and rolling 14 or better happens 35.49% of the time. Set the pool to 4d6, keep the highest 3, and read the distribution to see how quickly the odds fall away above 15.

What this calculator does not do

• It does not roll dice and it does not generate random numbers. It reports exact probabilities, so the numbers are the same every time you open the page.
• It assumes fair dice with equally likely faces. Loaded, rounded or biased dice are not modelled.
• Keep-highest and keep-lowest pools are limited to 12 dice with up to 20 sides each, which covers advantage, disadvantage and 4d6 keep highest 3. Larger pools can still be totalled with the first mode.
• It does not handle re-rolls, exploding dice, pools that count successes instead of adding up, or opposed rolls between two different pools. Work those out as two separate rolls and compare them.
• It never sends or stores your pool. Every probability is worked out in this page, in your browser, from the numbers you type.

Frequently asked questions

What are the odds of rolling a 15 or higher on a d20?

Six faces out of twenty get there, so a single d20 hits 15 or better 30.00% of the time. Roll two d20 and keep the higher and the chance rises to 51.00%, because the roll only fails when both dice come up 14 or less and that is 14/20 times 14/20. With disadvantage the same target succeeds just 49.00% of the time, since now both dice have to reach 15.

How do you work out the probability of rolling at least a number on 2d6?

Count the combinations that reach the number and divide by 36, because two six-sided dice have 36 equally likely outcomes. Rolling at least 9 means the ten combinations that total 9, 10, 11 or 12, so the chance is 10 in 36, or 27.78%. At least 7 is 21 in 36, or 58.33%. The calculator does that counting for any pool, including pools where dice are dropped, which is where counting by hand stops being practical.

What does 4d6 drop lowest average?

It averages 12.24, not the 14 a straight 4d6 would give you. Dropping the lowest die pulls the average down by about 1.76 because the discarded die is usually a low one, and it also lifts the floor: the worst you can roll improves from 4 to 3 plus three ones. The distribution is skewed towards the middle, with 18 needing three sixes on four dice, which happens 21 times in 1296, or 1.62%.

Is advantage the same as a plus three bonus?

No, and the difference matters at the extremes. Against a target of 11, advantage succeeds 75.00% of the time while a flat +3 succeeds 65.00%, so advantage is worth more there. Against a target of 20 the picture flips: advantage succeeds only 9.75% of the time because both dice still have to come up 20, while a +3 bonus succeeds 20.00% of the time. Advantage helps most in the middle of the range and does nothing for a roll that is out of reach.