Dice Roll Probability Calculator

Dice Roll Probability is evaluated from Number of Dice, Faces per Die and Target Sum. The calculation reports P, P as% and Total Outcomes.

Results

Thanks — we’ve logged this for review.

About the Dice Roll Probability Calculator

Dice Roll Probability is treated here as a quantitative relation between Number of Dice, Faces per Die and Target Sum and P, P as%, Total Outcomes and Favorable Outcomes.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Use dynamic programming to count the number of ways to reach each sum. Divide by total outcomes (f^n) to get probability.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Use dynamic programming to count the number of ways to reach each sum. Divide by total outcomes (f^n) to get probability.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Two D6 (standard dice): P(rolling a 7)

Inputs

num_dice: 2 num_faces: 6 target_sum: 7
P: 0.1667. P as%: 16.67%. Total Outcomes: 36. Favorable Outcomes: 6. Expected Sum: 7

With Number of Dice = 2, Faces per Die = 6 and Target Sum = 7 as the stated inputs, the result is P = 0.1667, P as% = 16.67% and Total Outcomes = 36. Each value corresponds to the declared output fields.

Example 2: D20 single die: P(rolling exactly 20 — critical hit)

Inputs

num_dice: 1 num_faces: 20 target_sum: 20
P: 0.05. P as%: 5%. Total Outcomes: 20. Favorable Outcomes: 1. Expected Sum: 10.5

With Number of Dice = 1, Faces per Die = 20 and Target Sum = 20 as the stated inputs, the result is P = 0.05, P as% = 5% and Total Outcomes = 20. Each value corresponds to the declared output fields.

Example 3: Three D6: P(sum equals 10)

Inputs

num_dice: 3 num_faces: 6 target_sum: 10
P: 0.125. P as%: 12.5%. Total Outcomes: 216. Favorable Outcomes: 27. Expected Sum: 10.5

With Number of Dice = 3, Faces per Die = 6 and Target Sum = 10 as the stated inputs, the result is P = 0.125, P as% = 12.5% and Total Outcomes = 216. Each value corresponds to the declared output fields.

Example 4: Two D10: P(sum = 15)

Inputs

num_dice: 2 num_faces: 10 target_sum: 15
P: 0.06. P as%: 6%. Total Outcomes: 100. Favorable Outcomes: 6. Expected Sum: 11

With Number of Dice = 2, Faces per Die = 10 and Target Sum = 15 as the stated inputs, the result is P = 0.06, P as% = 6% and Total Outcomes = 100. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate probability of rolling a specific sum
  • Find odds for board games and tabletop games
  • Learn about discrete probability distributions