Statistics and Probability
Roll standard or custom-sided dice, add a whole-number modifier and inspect every individual result instead of seeing only the final total.
Choose dice and sides, then roll.
Individual rolls will appear here.
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Each die is sampled separately using browser pseudorandomness. Do not use this tool for money, security, or regulated drawings.
Dice notation abbreviates the number and shape of dice. For example, 2d6 means roll two six-sided dice; 3d20+2 means roll three twenty-sided dice and add two to the sum. This roller supports any integer side count from 2 through 1,000, not just familiar tabletop dice.
The raw sum adds the individual die faces. A modifier is added only once after that sum, not to each die. A 2d6-1 roll of 3 and 5 gives 3 + 5 - 1 = 7. Keeping the faces visible lets you check the arithmetic and apply a game rule that depends on individual dice.
A single fair six-sided die has six equally likely faces, each with probability 1/6. For two six-sided dice, totals are not equally likely: 7 has six ordered combinations, whereas 2 has only one. This page simulates rolls and shows observed outcomes; it does not calculate exact distribution tables for custom dice.
The recent-roll list retains up to ten results in the open page. Reloading discards it. Browser pseudorandomness is suitable for casual practice and games, but not for secure drawings, wagers, or validated research sampling.
Final total = die 1 + die 2 + … + die n + modifier. Example: three d6 faces of 1, 4 and 6 with a -2 modifier produce 1 + 4 + 6 - 2 = 9.
For n dice with s equally likely faces, the minimum raw sum is n and the maximum is n × s. A modifier shifts both bounds by the same amount; it does not change which face each die can show.
The average face value for one ideal s-sided die labeled 1 through s is (s + 1) / 2. The average raw total for n such dice is n × (s + 1) / 2.
Roll common d4, d6, d8, d10, d12, d20 or d100 combinations and inspect the faces.
Repeat the same setup to compare an observed sequence with expected ranges and distribution shape.
Use a nonstandard number of sides for a mathematical model where outcomes are numbered 1 through s.
This is a browser simulation, not a certified physical die or cryptographically secure lottery system.
Roll two six-sided dice, add their face values, then add three once to obtain the final total.
Yes. A sufficiently negative modifier can make the final total below zero, even though each die face is at least one.
No. Individual faces are sampled uniformly, but multiple combinations can produce some totals more often than others.
No. It only removes the recent-roll list; your current result and settings remain visible.
Last reviewed: October 23, 2026. Calculations and simulations run in your browser; verify important decisions independently.
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