How is the probability calculated?

The tool uses dynamic programming (convolution) to count all possible combinations that produce each sum, then divides by the total number of outcomes. This gives exact probabilities, not estimates.

What does "at least X" mean?

"At least X" is the probability that your total roll (including modifier) is greater than or equal to X. This is the most useful metric for beating a target DC in RPGs.

Why does 2d6 feel more consistent than 1d12?

2d6 has a bell-curve distribution centered on 7, while 1d12 is flat (each value equally likely). The bell curve means mid-range results are far more probable with 2d6.

What is the range of supported dice?

Standard dice (d4, d6, d8, d10, d12, d20) plus any custom die from d2 to d100. You can roll 1 to 100 of them at once, and every probability is counted exactly with integer arithmetic.

What is the probability of rolling at least one 6?

One minus the chance that no die shows a 6: 1 − (5/6)^n. That is 16.67% with one die, 30.56% with two dice (11 of 36 outcomes), 42.13% with three and 51.77% with four, so you need four dice for better than even odds. Set the Individual Dice panel to face 6 and comparison = to see any dice count.

What are the odds of rolling doubles?

With two dice of s sides, s of the s² outcomes are doubles, so the chance is 1/s: 6/36 = 16.67% for 2d6 and 5% for 2d20. For n dice all showing the same face it is 1/s^(n−1), for example 1/36 = 2.78% for three six-sided dice.

How much does advantage help in D&D 5e?

Rolling two d20s and keeping the higher one changes the chance of meeting a target t from (21 − t)/20 to 1 − ((t − 1)/20)². Against DC 15 that is 51% instead of 30%, and disadvantage drops it to 9%. Advantage adds the most, 25 percentage points, at DC 11. The d20 table below lists every DC.

Does the modifier affect probabilities?

Yes. The modifier shifts the entire distribution up or down. For example, rolling 1d20+5 means all results are 5 higher, so hitting DC 15 requires only a roll of 10 or better.

What is the probability of rolling a 1 on a die?

One divided by the number of sides: 1/6 = 16.67% on a d6, 1/10 = 10% on a d10 and 1/20 = 5% on a d20. Set the dice count to 1 and look up a target of 1 to see it with exact fractions.

Can I mix die types or keep only the highest dice?

The sum view adds 1 to 100 dice of one type plus a flat modifier. The Individual Dice panel covers keeping the single highest or lowest die (at least one die ≥ X, or all dice ≥ X), which is how advantage and disadvantage work. Mixed pools such as d10 + d20, or 4d6 keeping the highest three, need a tool that models those rolls, such as AnyDice.

Dice Probability Calculator

Select dice type and count to see the exact distribution and odds for any sum, plus the chance that one, k or all dice show a number, and advantage or disadvantage odds.

Dice probability = ways to roll the result ÷ total outcomes (sides raised to the number of dice).

Dice Configuration

Die Type

Number of Dice

Modifier (±)

Target Sum Lookup

Enter a target value to see the probability of rolling exactly that sum or at least that sum.

Target Sum

Individual Dice

Chance that the dice above show a face value, e.g. at least one 6, exactly two 1s, or every die 4 or higher (disadvantage-style).

Face Value k dice

At least one die (highest die) —

Exactly k dice —

At least k dice —

All dice (lowest die) —

All dice show the same face —

Configure your dice and click Calculate

Probability distribution will appear here

Two dice (2d6) probability chart

All 36 outcomes of two six-sided dice. 7 is most likely because six combinations make it (1+6, 2+5, 3+4, 4+3, 5+2, 6+1).

Sum	Ways	Exactly	At least	At most
2	1/36	2.78%	100.00%	2.78%
3	2/36	5.56%	97.22%	8.33%
4	3/36	8.33%	91.67%	16.67%
5	4/36	11.11%	83.33%	27.78%
6	5/36	13.89%	72.22%	41.67%
7	6/36	16.67%	58.33%	58.33%
8	5/36	13.89%	41.67%	72.22%
9	4/36	11.11%	27.78%	83.33%
10	3/36	8.33%	16.67%	91.67%
11	2/36	5.56%	8.33%	97.22%
12	1/36	2.78%	2.78%	100.00%

d20 odds with advantage and disadvantage

Chance to roll the target or higher on a d20 (before modifiers). Advantage keeps the higher of two d20s: 1 − ((t − 1)/20)². Disadvantage keeps the lower: ((21 − t)/20)².

Need	Normal	Advantage	Disadvantage
2+	95.00%	99.75%	90.25%
3+	90.00%	99.00%	81.00%
4+	85.00%	97.75%	72.25%
5+	80.00%	96.00%	64.00%
6+	75.00%	93.75%	56.25%
7+	70.00%	91.00%	49.00%
8+	65.00%	87.75%	42.25%
9+	60.00%	84.00%	36.00%
10+	55.00%	79.75%	30.25%
11+	50.00%	75.00%	25.00%
12+	45.00%	69.75%	20.25%
13+	40.00%	64.00%	16.00%
14+	35.00%	57.75%	12.25%
15+	30.00%	51.00%	9.00%
16+	25.00%	43.75%	6.25%
17+	20.00%	36.00%	4.00%
18+	15.00%	27.75%	2.25%
19+	10.00%	19.00%	1.00%
20+	5.00%	9.75%	0.25%

Method, scope and privacy

For fair identical dice, this calculator counts every outcome with exact integer convolution, then divides each count by the exact outcome total. Exact, at-least and at-most views therefore use the same distribution rather than simulation. Individual-dice results use the binomial count C(n, k) · m^k · (s − m)^(n − k), where m is the number of faces that meet the condition.

Privacy: dice configuration and results remain in this browser tab. No roll inputs are sent to a calculation service.

Quick answer

Dice probability = ways to roll the result ÷ total outcomes (sides raised to the number of dice). Two six-sided dice have 6 × 6 = 36 outcomes, and 6 of them total 7, so a 7 has a 6/36 = 16.67% chance and is the most likely sum.

Examples

2d6 sum	Exactly	At least
7	16.67%	58.33%
8	13.89%	41.67%
10	8.33%	16.67%
11	5.56%	8.33%
12	2.78%	2.78%

Pick a die, dice count and modifier to chart exact, at-least and at-most odds for every sum.

Summary