Type a dice pool into the calculator above and it returns the full picture: the chance of hitting an exact total, the cumulative odds of rolling that total or better, the average and median result, the spread, and the complete distribution. It handles any number of dice with any number of sides, plus modifiers and keep-highest or drop-lowest rules.
What the calculator gives you
Every result comes from counting outcomes, not from simulation, so the numbers are exact rather than approximate.
The exact-total figure answers “what are the chances of landing on precisely this number?” That’s the one you want for a Catan hex or a specific craps point.
The at-least and at-most figures are cumulative. At-least sums every outcome from your target up to the ceiling, which is the shape of almost every roll in a role-playing game. At-most does the reverse and matters when a low roll is what you want, such as a roll-under system.
Mean and median describe the center. For symmetric pools like 2d6 they land on the same value, and they part company as soon as you add a keep or drop rule.
Standard deviation describes the spread. A high one means a swingy pool where single rolls often land far from average. Two pools can share an average and feel completely different at the table because of this number.
The distribution is every possible total with its probability, which is the chart the other figures are summarizing.
Three worked examples
A 2d6 total. Two six-sided dice give 36 equally likely outcomes across totals from 2 to 12, with an average of 7. Ask for the chance of exactly 9 and you get 11.11%, or 4/36 of the grid. Ask for 9 or better and it jumps to 27.78%, because that now includes 10, 11 and 12. The full two-dice chart walks through every total.
A d20 check needing 15 or better. Enter 1d20 and set the target to 15. The answer is 30%. The 5e Dungeon Master’s Guide treats DC 15 as a medium task, and that percentage is why: an unskilled character fails it most of the time.
Now give the character a +5 to the roll. Enter 1d20+5 against the same target and the odds climb to 55%. On a flat die, every point of bonus is worth exactly 5% of success, which is what makes d20 modifiers so easy to price. That flatness disappears the moment you roll more than one die.
Advantage works differently. Rolling two d20s and keeping the better one is 2d20kh1, and the chance of clearing 15 becomes 51%. The average of a single d20 is 10.5; with advantage it rises to 13.83.
4d6 drop lowest for D&D stats. The classic ability-score method rolls four six-sided dice and throws away the worst one. Enter 4d6d1. The average score is 12.24, against 10.5 for three straight dice. Discarding the worst die buys you that difference.
The distribution is where it gets interesting. Median comes in at 12 and the standard deviation is 2.85, tighter than the 2.96 of a plain 3d6. Dropping a die pushes the whole curve up and squeezes it. The chance of any single score reaching 15 or better is 23.15%, and an 18 lands at 1.62%. If you want the six scores rolled for you rather than the math behind them, the stat roller does that directly.
The notation the calculator accepts
The input follows standard dice notation, the same shorthand printed in rulebooks.
NdM is the base form: N dice with M sides each. 3d6 is three six-sided dice. 1d20 is one twenty-sider. 2d10 is a pair of tens.
Add or subtract a flat number with + or -. 1d20+5 adds five to the result. 2d6-1 takes one off.
kh keeps the highest dice and d drops the lowest. 2d20kh1 rolls two twenty-siders and keeps the better, which is advantage in fifth edition D&D. 4d6d1 rolls four six-siders and drops the worst, which is the ability-score method above. The digit after the letters is how many dice to keep or drop, so 5d6d2 throws away the two lowest of five.
A full breakdown of the format, including the pieces this calculator doesn’t need, lives on the dice notation page.
Reading the answer sensibly
A percentage tells you what happens across many rolls. It says nothing about the next one. A hex on 13.89% can go ten turns without paying out, and nothing is broken when it does.
Where the calculator earns its keep is in comparing options before you commit. Is a 5 hex plus a 9 hex better than a single 6 hex? Is a +2 bonus worth more than advantage on this check? Those questions have exact answers. The dice probability basics page covers the reasoning if you’d rather work it out by hand.
FAQ
How do I calculate dice probability by hand?
Count the outcomes that give you what you want, then divide by the total number of outcomes. Two six-sided dice have 36 outcomes, and 6/36 of them total 7, which gives 16.67%. Larger pools get painful fast, which is what the calculator is for.
What does 4d6 drop lowest average?
It averages 12.24 per score, compared to 10.5 for three dice with nothing dropped. The extra die shifts results upward and narrows the spread, with a standard deviation of 2.85. That’s why the method produces heroes rather than ordinary people.
What are the odds of rolling 15 or higher on a d20?
30% on a flat roll. Each face of a twenty-sided die is equally likely at 5%, so cumulative odds move in even steps. With advantage, rolling 2d20kh1, the same target clears 51% of the time.
Are the results exact or simulated?
Exact. The calculator enumerates outcomes and counts them rather than rolling a virtual die thousands of times, so a fraction like 6/36 is the real count and not an estimate. Everything runs in your browser, with nothing sent to a server.