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Dice Roll Probability

P(sum s on n d6). Free online Dice Roll Probability. Calculate dice roll probability online — fast, accurate, mobile-friendly, no signup needed.

Each outcome has equal probability 1/6.
Probability
16.6667%

Derivation

  1. ├── 01Givenn = 2, s = 7
  2. ├── 02Formulan / r × 100
  3. ├── 03Substitute2 / r × 100
  4. └── 04Compute Probability16.666667
Did you know?

Probability theory traces to the Pascal–Fermat letters (1654) about a gambling dispute over how to fairly split a prize if a game is interrupted.

§01What is

Understanding the Dice Roll Probability

The Dice Roll Probability computes Probability from 2 inputs: dice count, target sum. P(sum s on n d6).

Games and puzzles mix math with pattern-spotting. Whether it’s a lottery combination, a dice probability, or a game-theory decision, the numbers behind the fun are worth running properly. The Dice Roll Probability sits in that toolkit — it P(sum s on n d6). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

n / r × 100

Where

n
Dice count
s
Target sum
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Dice count = 2, Target sum = 7.

  1. 01Start by noting the input — Dice count: 2.
  2. 02Start by noting the input — Target sum: 7.
  3. 03Substitute these values into the formula: n / r × 100
  4. 04Compute Probability: the calculator returns 16.6667.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Dice Roll Probability Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Dice count halved

n = 1 (from 2)

Keep every other input at its default and halve the dice count. See how probability responds.

  1. 01New Dice count: 1
  2. 02Baseline Probability: 16.6667
  3. 03New Probability: 0
  4. 04Probability decreases by 100% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Dice count doubled

n = 4 (from 2)

Keep every other input at its default and double the dice count. See how probability responds.

  1. 01New Dice count: 4
  2. 02Baseline Probability: 16.6667
  3. 03New Probability: 1.54321
  4. 04Probability decreases by 90.7% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Target sum halved

s = 3.5 (from 7)

Keep every other input at its default and halve the target sum. See how probability responds.

  1. 01New Target sum: 3.5
  2. 02Baseline Probability: 16.6667
  3. 03New Probability: 0
  4. 04Probability decreases by 100% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Target sum doubled

s = 14 (from 7)

Keep every other input at its default and double the target sum. See how probability responds.

  1. 01New Target sum: 14
  2. 02Baseline Probability: 16.6667
  3. 03New Probability: 0
  4. 04Probability decreases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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