Dice Probability Calculator

Two six-sided dice total 7 about 16.667% of the time — 6 of the 36 ways they can land, or roughly 1 in 6. That is the question most people arrive with, and it is answered before you touch anything. Change the dice, the die type, or the total, and the answer moves as you type. What makes this different from the rest of the results you just scrolled past is the chart underneath. It shows every total those dice can produce and how likely each one is, all at once. So the moment you have asked whether 11 is more likely than 12, you can already see that it is — twice as likely, 5.556% against 2.778% — without running a second calculation. The tools that rank above this one split into two camps, and both of them cost you something. The powerful ones hand you a scripting language and ask you to write `output 2d6` before they will answer a one-line question, which is a real barrier for a student checking homework at eleven at night. The simple ones give you a three-field form wrapped in ad units, answer exactly one question, and send you back to the search results for the next one — because one question per pageview is the business model, not a limitation. This is the third option: a form with nothing to learn, and every neighbouring answer already on screen. There is also a second mode for the question dice games actually turn on — not what the dice add up to, but how many of them show a particular face. The chance of at least one 6 in four rolls, or exactly two 6s in five. Same screen, same absence of syntax.

Built by Bob QA by Ben Shipped September 21, 2026

How to use

1
Start in Sum of dice, which is where the page opens. Set how many dice you are rolling and what kind — d4 through d100, with d6 selected because that is what most questions are about. The answer updates on every keystroke; there is no Calculate button to hunt for.
2
Choose whether you want the total to be exactly, at least, or at most your target. That third option matters more than it looks: 'at most 8' and 'exactly 8' are very different questions, and most calculators make you run them separately or do not offer the comparison at all.
3
Type the target sum. If you ask for something the dice cannot reach — 13 on two six-sided dice — you get 0% and a sentence explaining why, rather than a blank box or a NaN. The hint under the field always tells you the range those dice can actually produce.
4
Read the answer three ways. The big number is the percentage to three decimals. Underneath, the same value as 1-in-N odds, which is easier to hold in your head, and as an exact fraction, which is what you want if you are checking work or writing it up. On very large rolls the fraction is left out rather than rounded, because there is no exact fraction that a number can hold.
5
Look at the distribution chart. Every possible total gets a bar, and the ones matching your question are highlighted in green. This is where the questions you did not think to ask get answered — where the peak sits, how fast the tails fall away, whether two totals you assumed were close really are.
6
Switch to Matching faces for the other kind of dice question: how many dice show a particular number. Set how many dice you are rolling, whether you want at least or exactly that many matches, and which face. This is the D&D saving throw, the Yahtzee question, and the one that founded probability theory as a field.
7
Hit Copy to take the whole answer — the question, the percentage, the fraction and the odds — as one line of plain text, ready to paste into homework, a rules argument, or a message to whoever you are betting against.

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Frequently asked questions

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

16.667%, or 6 in 36, or about 1 in 6. Seven is the most likely total on two six-sided dice, and the reason is that it has the most ways of happening: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. Every other total has fewer. Twelve has exactly one route (6+6), which is why it turns up 2.778% of the time — six times rarer than a 7. This is the whole of why craps, Monopoly and Settlers of Catan feel the way they do: the totals are not equally likely, and the board is built around that fact.

Is it more likely to roll an 11 or a 12?

An 11, by exactly double. Eleven can happen two ways — 5+6 and 6+5 — for 5.556%, while 12 can only happen one way, 6+6, for 2.778%. The trap is that 5+6 and 6+5 feel like the same roll when you look at the dice on the table, but they are two distinct outcomes out of the 36 the dice can produce, and the arithmetic counts them separately. Every total except 7 has a partner on the other side of the peak with identical odds: 11 matches 3, 12 matches 2, 10 matches 4. The distribution is a perfect triangle, which the chart makes obvious in a way a single percentage never does.

Why isn't every total equally likely?

Because you are adding, and addition loses information. A single die is genuinely uniform — each of its six faces is equally likely, which is why the chart for one die is flat. The moment you add a second die, you start collapsing different rolls into the same total, and you collapse them unevenly. Only one of the 36 combinations adds to 2, but six of them add to 7. Add a third die and the effect strengthens; by the time you are rolling ten dice the distribution is close enough to a bell curve that statisticians use dice to demonstrate the central limit theorem. If you want uniform odds, you want one die, or you want the Matching faces mode, where every face really is equally likely.

What are the odds of at least one 6 in four rolls?

51.775%, or 671 out of 1,296. This specific number is where probability theory started. In 1654 a French gambler, the Chevalier de Méré, had been making money for years betting that he would see at least one 6 in four rolls of a single die — a bet that wins just over half the time. He then reasoned that betting on at least one double-six in 24 rolls of two dice should work the same way, since 24 is to 36 what 4 is to 6. It does not: that one comes to 49.14%, and it lost him money steadily. He wrote to Blaise Pascal about it, Pascal wrote to Pierre de Fermat, and the correspondence that followed is generally taken as the founding of probability as a discipline. The mistake is a real one and people still make it: chances do not add, they compound. Four rolls at 1-in-6 is not 4/6.

How do you work this out by hand?

For 'at least one', the fast route is to calculate the opposite and subtract. The chance of no 6 in one roll is 5/6; for four independent rolls that is (5/6)⁴ = 625/1296, so at least one 6 is 1 − 625/1296 = 671/1296. Working out 'at least one' directly means adding up the cases for exactly one, exactly two, exactly three and exactly four, which is four times the work for the same answer. For sums, there is no shortcut as clean: you count the combinations that reach your target and divide by the total, which for two dice is easy enough to do on paper and stops being practical around four. That counting is what this page does for you, one die at a time, and it is why it can handle fifty dice without slowing down.

What's the difference between 16.667% and 1 in 6?

Nothing mathematically — they are the same number written two ways — but they are not equally useful. A percentage is better for comparing two chances, because your eye can rank 16.667% against 5.556% instantly. Odds are better for deciding whether to take a bet, because '1 in 6' maps onto something you can picture happening. The exact fraction is better for showing your work, and it is the only one of the three that is not rounded at all: 6/36 is precisely true, while 16.667% is a three-decimal approximation of 16.666…% repeating forever. All three are on screen because which one you want depends on what you are about to do with it.

Why does the exact fraction disappear on very large rolls?

Because past a certain size there is no fraction a computer can hold without lying to you. The denominator is the total number of ways the dice can land, which is the number of sides raised to the number of dice. Twenty six-sided dice is 6²⁰, about 3.66 quadrillion — large, but still exactly representable, so you get an exact fraction. Fifty hundred-sided dice is 100⁵⁰, a 1 followed by a hundred zeros, and no ordinary number in any programming language holds that precisely. Rather than print a fraction that is quietly wrong in its last fifteen digits, this leaves it out and tells you why. The percentage and the odds are still exact to the precision shown, because those are computed a different way — by combining probabilities die by die, which never needs the enormous total at all.

Does this handle advantage, exploding dice, or keeping the highest?

No, and that is on purpose. Advantage in D&D, exploding dice in Savage Worlds, and keep-highest-three-of-four in character generation are all real questions, and they all need you to describe a procedure rather than a roll. The tools that answer them give you a small programming language to describe that procedure in, which is a fair trade if you are designing a game system and a poor one if you want to know the odds of a 7. This page does one job — the odds of a straight roll of fair dice — and does it without asking you to learn anything first. If you need the procedural cases, the notation-based tools genuinely are the right instrument.

Are real dice actually fair?

Casino dice are close. They are machined to tight tolerances, the pips are drilled and filled with material of the same density as the body, and the edges are left sharp so they tumble rather than roll — which is why they look and feel different from the dice in a board game box. Ordinary moulded plastic dice are not nearly as good: the pips are hollow, which makes the 6 face very slightly lighter than the 1 face, and cheap d20s are the worst offenders because a moulded twenty-sided solid is hard to keep balanced. The bias is small — small enough that you would need thousands of rolls to detect it, and far smaller than the effect of how you throw. Every number here assumes perfectly fair dice, which is the right assumption for homework and a close enough one for game night.

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Dice Probability Calculator

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