Quick rolls
Dice controls
Tabletop presets
Batch results
| # | Expression | Dice | Base | Modifier | Final | Successes | Failures |
|---|---|---|---|---|---|---|---|
| Roll dice to populate this table. | |||||||
Roll statistics
Final result frequency
| Result | Frequency | Percentage |
|---|---|---|
| No data yet. | ||
Probability analysis
Roll a supported expression to calculate its exact distribution.
Session roll history
History stays in this browser tab until the session ends.
Formula used
For ordinary dice, each kept die contributes its rolled face value. The base total adds signed dice groups and numeric notation modifiers. The global modifier is then added. Multiplication and division are applied afterward. Optional minimum and maximum limits clamp the final result.
For one fair die with s sides, each face has probability 1 / s. The expected value is (s + 1) / 2. Independent dice distributions combine through convolution.
How to use this calculator
- Enter notation like 2d6+3 or choose a quick roll.
- Select advantage, modifiers, rerolls, explosions, or thresholds when needed.
- Choose secure randomness or a reproducible seeded sequence.
- Set batch repetitions when you want statistics across many rolls.
- Press Roll Dice and review the result above the form.
- Use CSV, PDF, copy, or print actions to save results.
Dice notation examples
| Notation | Meaning | Typical use |
|---|---|---|
| 1d20 | Roll one twenty-sided die. | Checks and attacks. |
| 4d6+3 | Roll four six-sided dice then add three. | Damage or totals. |
| 2d20kh1 | Roll two D20 dice and keep highest one. | Advantage. |
| 2d20kl1 | Roll two D20 dice and keep lowest one. | Disadvantage. |
| 4d6dl1 | Roll four D6 dice and drop lowest one. | Ability scores. |
| 1d6! | Roll D6 and explode on its maximum face. | Exploding systems. |
| 4dF | Roll four Fate dice using minus zero plus. | Fate and Fudge games. |
About the Dice Roller
A dice roller replaces physical dice with fast digital randomness. Standard notation makes complicated rolls easier to repeat accurately. Disadvantage keeps the lower result instead.
Keep and drop rules help with character creation methods. Exploding dice continue rolling after the maximum face appears. Reroll controls replace selected values once during each roll. Critical indicators highlight natural ones and twenties on D20 rolls. Fate dice provide negative neutral and positive outcomes.
Secure mode uses server generated cryptographic random integers. Seeded mode creates reproducible sequences for testing repeated scenarios. Batch rolling repeats an expression many times automatically. Those repeated totals create useful descriptive statistics. Mean median mode minimum and maximum summarize the sample.
The probability panel analyzes supported ordinary additive dice expressions. Expected value describes the average result across many trials. Target analysis measures chances for exact or greater outcomes. A compact distribution chart shows how likelihood changes across totals. Advanced modifiers can make exact distributions substantially more complicated. The tool reports when exact analysis becomes unavailable.
Session history stores recent rolls inside the current browser tab. Each history item preserves notation totals and rolling settings. Repeating a saved roll restores those options quickly. Custom presets also preserve frequently used tabletop configurations. Quick buttons cover standard dice without requiring typed notation. Custom sides handle unusual systems such as D7 rolls. Keyboard users can submit the form using Enter.
CSV exports are useful for spreadsheets and later analysis. PDF exports create a compact printable record of results. Printing can also produce a browser generated PDF file. Visual dice make individual outcomes easier to scan quickly. Dropped dice appear faded while exploding dice receive markers. Rerolled dice receive separate markers for transparency. Animation and sound remain optional for accessibility.
Fair digital rolling depends on trustworthy random number generation. Secure mode avoids predictable client generated pseudo random sequences. Seeded mode is intentionally predictable when testing needs repetition. Probability calculations assume fair independent dice unless modifiers intervene. Physical dice can behave differently because manufacturing affects balance. Digital results avoid those physical imperfections during repeated simulations.
Dice rollers support games probability lessons and simple decisions. Tabletop players can prepare reusable attack and damage presets. Teachers can demonstrate distributions using large batch samples. Developers can reproduce test cases with fixed random seeds. Export tools make those experiments easier to document. Clear notation validation prevents silent mistakes during complicated expressions. Reliable dice rolling keeps every game moving smoothly today.