Dice Roller Calculator

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Roll virtual dice, see every die and the combined total, then check your exact chance of meeting a target.

Advanced options
Rolled totalThe dice are added before the modifier is applied once.
Individual die resultsValues are shown in roll order, before the modifier.
Lowest possible total
Highest possible total
Expected average totalThis is the long-run average over many rolls.
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How to use our Dice Roller Calculator

  1. Choose "Choose dice" to enter separate values, or choose "Use dice notation" to enter an expression such as 2d6+3.
  2. Enter the number of dice and sides for the builder, or copy the dice expression from your game rule or character sheet.
  3. Open "Advanced options" if you need a flat modifier, want to check a target chance, or need a repeatable roll code.
  4. Click "Calculate" to generate a roll and view the rolled total, individual dice, possible range, and expected average.
  5. Sanity-check the roll by confirming that the rolled total is between the displayed lowest and highest possible totals.
Example inputs for Dice Roller Calculator
Example inputs for Dice Roller Calculator

Definitions

Dice notation (NdS): A short dice description. N is the number of dice and S is the number of sides, so 2d6 means two six-sided dice.

Flat modifier: A signed number added or subtracted once after the dice are totaled. In 2d6+3, the modifier is +3.

Target total: The final total a game rule asks you to meet, stay at or below, or hit exactly. It includes any flat modifier.

Exact target chance: The number of favorable outcomes divided by the number of all equally likely outcomes, written as a reduced fraction.

Expected average: The long-run average total across many rolls. It does not predict the next roll.

Repeatable roll code: A whole-number code that recreates the same dice sequence for an example or test.

Ways to total 2d6Each total has a different number of equally likely outcomes. Totals near 7 occur more often than the lowest and highest totals.Ways to total 2d6Each total has a different number of equally likely outcomes.2 or 121 outcomes3 or 112 outcomes4 or 103 outcomes5 or 94 outcomes6 or 85 outcomesRolled total
Ways to total 2d6
Totals near 7 occur more often than the lowest and highest totals.

Common mistakes and quick fixes

Mistake: Reading 2d6 as the number twenty-six.
Fix: Read 2d6 as two six-sided dice. Add the two rolled values.

Mistake: Applying a flat modifier to every die.
Fix: "Add or subtract after rolling (points)" is applied once after all dice are added.

Mistake: Entering a die shape instead of its face count.
Fix: Enter 6 for a d6 or 20 for a d20. The field needs the number of sides.

Mistake: Treating target chance as a prediction of the roll already shown.
Fix: Target chance counts every possible outcome. It does not change or explain the displayed random roll.

Mistake: Using a repeatable roll code for a roll that must be unpredictable.
Fix: Leave "Repeatable roll code" blank for a new browser-generated roll. A code recreates the same sequence.

Mistake: Entering keep, drop, or exploding-die codes.
Fix: Use dice terms such as 2d6 or 1d20+1d4, with an optional final whole-number modifier.

Limitations & Key Assumptions / Boundary Conditions

  • Each die is treated as fair and independent, with every face equally likely.
  • The calculator accepts up to 100 dice and up to 1,000 sides on each die.
  • Dice notation accepts dice terms joined by plus signs and an optional final whole-number modifier. It does not support keep, drop, reroll, exploding dice, multiplication, division, decimals, or ranges.
  • Target odds are exact for the entered dice model, but game rules involving advantage, critical hits, special faces, or rerolls can change the real chance.
  • A blank repeatable roll code uses browser cryptographic randomness when available. A supplied code is predictable and intended only for repeatable examples.
  • A target outside the possible range is valid. Its exact chance can be 0% or 100%.

Methodology

Roll calculation

The calculator builds the active dice list from the separate fields or the dice notation. It generates one whole value from 1 through the side count for every die, adds those values, then applies one flat modifier.

rolled total = sum of individual die values + flat modifier

For example, 2d6+3 has two six-sided dice and one modifier. If the dice show 2 and 2, the rolled total is 2 + 2 + 3 = 7.

Range and average

The lowest total uses a 1 on every die. The highest total uses the largest face on every die. The expected average adds the average of each fair die, then applies the modifier once.

lowest possible total = number of dice + flat modifier

highest possible total = sum of all die side counts + flat modifier

average of one S-sided die = (S + 1) / 2

For 2d6+3, the possible range is 5 through 15 and the expected average is 10 points.

Target chance

When a target check is selected, the calculator counts every equally likely dice outcome that meets the chosen condition. It uses the full distribution of possible totals, not a simulation and not the random roll displayed above.

target chance percent = 100 x favorable outcomes / total outcomes

exact target chance = favorable outcomes / total outcomes, reduced

For 2d6+3, rolling at least 8 means the two dice must total at least 5. Thirty of 36 possible dice outcomes work, so the chance is 30/36, reduced to 5/6, or 83.33%.

Repeatable rolls

A blank roll code requests fresh browser cryptographic random values. With a roll code, the calculator advances a 32-bit repeatable sequence once for each die, so the same code and dice setup reproduce the same individual results.