Dice Probability Calculator

Pick your dice, pick the question, and read the odds. Totals, ranges, how many dice have to match, whether every die clears a number, and the two-d20 advantage and disadvantage rolls are all here. Underneath the answer sits the part most dice tools leave out: the full odds table for the dice you entered, not a fixed two-dice chart. Change 2d6 to 4d8 and every row and every bar changes with it. See the two-dice table, the math behind it, the at-least-one trap, and how advantage really shifts the odds.

How many dice

Dice type

2d6

Work out the chance that

Total

Rolling 2d6

16.6667%

That is 1/6 of every possible roll, about 1 in 6. You would expect one every 6 rolls, and there is a better than even chance of seeing it within 4.

As a decimal: 0.1666667
Odds against: 5 to 1
Possible totals: 2 to 12

P(sum = t) = ways to make t ÷ total outcomes

P(sum = 7) = 6 ÷ 36 = 0.1666667

Every total 2d6 can roll

Each bar is the chance of that exact total. The gold bars are the ones your question adds up, so the shaded area is the percentage above.

Total	Ways	P(=)	P(≥)	P(≤)	Odds
2	1	2.7778%	100%	2.7778%	1 in 36
3	2	5.5556%	97.2222%	8.3333%	1 in 18
4	3	8.3333%	91.6667%	16.6667%	1 in 12
5	4	11.1111%	83.3333%	27.7778%	1 in 9
6	5	13.8889%	72.2222%	41.6667%	1 in 7.2
7	6	16.6667%	58.3333%	58.3333%	1 in 6
8	5	13.8889%	41.6667%	72.2222%	1 in 7.2
9	4	11.1111%	27.7778%	83.3333%	1 in 9
10	3	8.3333%	16.6667%	91.6667%	1 in 12
11	2	5.5556%	8.3333%	97.2222%	1 in 18
12	1	2.7778%	2.7778%	100%	1 in 36

Two dice: every total and its odds

Two six-sided dice have 36 equally likely outcomes. Counting how many of them reach each total gives the whole table. Seven wins with 6 combinations; the two ends have one each.

Total	Combinations	Probability	Percent	Odds
2	1	1/36	2.7778%	1 in 36
3	2	2/36	5.5556%	1 in 18
4	3	3/36	8.3333%	1 in 12
5	4	4/36	11.1111%	1 in 9
6	5	5/36	13.8889%	1 in 7.2
7	6	6/36	16.6667%	1 in 6
8	5	5/36	13.8889%	1 in 7.2
9	4	4/36	11.1111%	1 in 9
10	3	3/36	8.3333%	1 in 12
11	2	2/36	5.5556%	1 in 18
12	1	1/36	2.7778%	1 in 36

Rolling for a 7 in craps, that works out to one every 6 rolls on average, with a better than even chance of seeing one inside 4.

The math behind a dice roll

Every roll of n dice with s faces has sⁿ equally likely outcomes. A probability is the count of outcomes you want over that total.

P(one die shows v) = 1/s
P(every die ≥ v) = ((s − v + 1)/s)ⁿ, because the dice are independent
P(at least one shows v) = 1 − ((s − 1)/s)ⁿ, the complement of missing every time
P(exactly k dice show v) = C(n, k) × (1/s)^k × ((s − 1)/s)^{n − k}, which is the binomial formula
P(sum = t) has no one-line formula. This tool builds it by taking the distribution of the running total and folding in one more die at a time, which is exact and needs about n × s × t operations instead of the sⁿ rolls that listing them would take.

That last point is why 10d6 is instant here: 60 million outcomes listed one by one, against a few thousand operations folded together.

At least one, and why it never reaches certainty

Adding 1/6 for each die is the most common dice mistake there is. It says six dice guarantee a six, and that seven dice make the probability larger than one. What actually happens is that each die independently fails to be a six five times in six, so the misses multiply.

Dice rolled	At least one six	Adding 1/6 per die would say
1d6	16.6667%	16.6667%
2d6	30.5556%	33.3333%
3d6	42.1296%	50%
4d6	51.7747%	66.6667%
6d6	66.5102%	100% (impossible)
10d6	83.8494%	100% (impossible)

Ten dice still leave a 16.1506% chance of no six at all. The gap between the two columns is exactly the probability of rolling two or more sixes, which the naive sum counts twice.

Advantage and disadvantage on a d20

Advantage rolls 2d20 and keeps the higher, so a check fails only when both dice miss: 1 − ((v − 1)/20)². Disadvantage keeps the lower and needs both to clear the number: ((21 − v)/20)². The effect is largest in the middle of the range, where there is the most room to move.

Need	One d20	Advantage	Disadvantage	Advantage gains
5+	80%	96%	64%	+16%
10+	55%	79.75%	30.25%	+24.75%
12+	45%	69.75%	20.25%	+24.75%
15+	30%	51%	9%	+21%
18+	15%	27.75%	2.25%	+12.75%
20+	5%	9.75%	0.25%	+4.75%

A DC 11 check gains the most from advantage, at roughly 25 percentage points. Needing a 20 gains under 5, because there is very little probability to double up on.

Three rolls worked out

Craps: rolling 9 or better

Totals of 9, 10, 11 and 12 have 4, 3, 2 and 1 combinations. That is 10 of 36, or 27.7778%.

Catan: the odds behind the numbers on the board

The pips under each number are its combination count. A 6 or 8 hits 13.8889% of rolls against 5.5556% for a 3, which is why they are worth roughly two and a half times as much per turn. Seven, the robber, is the most frequent of all at 16.6667%.

Yahtzee in one throw

The first die sets the target and the other four have to match it, so the chance is (1/6)⁴ = 0.0007716, about 1 in 1296 throws.

How this calculator is checked

The two-dice table, the at-least-one table and the advantage table are all generated at build time by the same solve() the calculator runs, so the copy cannot drift from the tool.
Sums are computed exactly by convolution rather than by simulating rolls, so a one-in-a-billion outcome is reported precisely instead of being missed by a sample.
Where the total outcome count still fits a JavaScript integer, the exact fraction is shown; past that point the page shows the decimal rather than a rounded fraction.
Impossible questions return zero rather than a blank: a total below the minimum, a face the die does not have, or more matching dice than were rolled.
Everything runs in your browser. Nothing you enter is stored or sent to a server.

Last reviewed: October 2026. Found an error? Report it and we'll fix it.

Frequently Asked Questions

What are the odds of rolling a 7 with two dice?

There are 6 ways to make 7 out of 36 equally likely rolls, which is 0.1666667 or 16.6667%. Seven is the most likely total on 2d6 because it has more combinations behind it than any other: 1+6, 2+5, 3+4 and the three reversed. Two and twelve sit at the other end with one combination each.

How many possible outcomes are there with two dice?

36. Each die has 6 faces and the dice are independent, so 6 × 6 = 36 ordered pairs. Ordered is the part people drop: 2 then 5 is a different outcome from 5 then 2, and counting them once turns 36 outcomes into 21 and every answer wrong.

How do you calculate dice probability?

Divide the outcomes you want by the total outcomes, which is faces to the power of dice. For a specific total, count the combinations that reach it. This tool does that by combining one die's distribution into the running total once per die, which is exact and fast enough to handle 100 dice, rather than listing every roll.

What is the probability of rolling at least one six?

Work out the chance of no sixes and subtract it from 1. With 4 dice that is 1 − (5/6)^4 = 51.7747%. The common mistake is to add 1/6 per die, which reaches certainty at six dice. It never does: even with 10 dice the chance is 83.8494%.

How does advantage work in D&D?

Advantage rolls two d20 and keeps the higher, so you fail only if both dice miss. Against a DC of 15 a single d20 succeeds 30% of the time and advantage lifts that to 51%. Disadvantage keeps the lower and needs both dice to clear the number, dropping it to 9%. Advantage helps most in the middle of the range and least at the extremes.

Why is the distribution of three or more dice a bell curve?

Middle totals can be reached in many more ways than extreme ones, and adding dice multiplies that effect. On 3d6 there is one way to roll 3 and 27 ways to roll 10, so the peak sits at 12.5% while each end is 0.463%. Keep adding dice and the shape approaches a normal curve.

What are the odds of rolling a Yahtzee on the first throw?

Five matching dice on one throw is 0.0007716, about 1 in 1296. The first die can be anything, then each of the other four has to match it: (1/6)^4. Real Yahtzee gives you three throws and lets you keep dice, which raises the odds considerably.

Can this calculator handle non-standard dice?

Yes. Pick Custom and set any number of faces from 2 to 1000, and roll up to 100 of them. The faces are assumed to be numbered 1 upward and equally likely. Dice with repeated or skipped numbers, and rules like exploding dice or rerolls, are outside what this handles.

Does rolling more dice make a particular total more likely?

It changes which totals are reachable and reshapes the odds rather than simply improving them. Adding dice raises the minimum and the maximum and concentrates probability in the middle, so a fixed target like 7 gets less likely once the average total passes it. Change the dice count in the tool and watch the whole table move.

Are the results simulated?

No. Nothing here rolls virtual dice. Every figure is the exact probability, computed from the combinations, so running the same question twice always gives the same answer and rare outcomes are reported precisely instead of being missed by a sample.

For events that are not dice, the probability calculator handles P(A and B), P(A or B) and conditional probability with the working shown. For repeated yes-or-no trials at any success rate, like coin flips or free throws, use the binomial distribution calculator, which is the same math as the matching-dice modes here at a general probability.

Related Calculators

📐

Pythagorean Theorem

Solve a² + b² = c² for any missing side of a right triangle, with the …

🧮

Scientific Calculator

Full scientific calculator with trigonometry, logarithms, exponents, f…

🏷️

Percent Off Calculator

Find the sale price and what you save for any percent off. Stack extra…

∪

Vertex Form Calculator

Convert standard form to vertex form and back, with the completing-the…