Dice Probability Calculator

This dice probability calculator finds the exact chance of rolling a particular total with several dice, such as a 7 with two six-sided dice. It counts the ways to make every total one die at a time, then divides favourable outcomes by all outcomes. It works for any number of sides, including d4, d8, d12 and d20.

Try:

How to use the dice probability calculator

  1. Enter the number of dice and the sides on each.
  2. Enter the target total and choose =, ≤ or ≥.
  3. Press Calculate to see the probability and the chart.

Formula

P=favourable outcomestotal outcomesP = \frac{\text{favourable outcomes}}{\text{total outcomes}}

Worked example: Two dice total 7

  • Number of dice: 2
  • Sides per die: 6
  • Target total: 7
  • Find: P(total = target)

✓ Answer checked

P(total=7)=16≈0.16666667P(\text{total} = 7) = \frac{1}{6} \approx 0.16666667
Favourable outcomes
6 of 36
As a percentage
16.6667%
Most likely total
7
00.050.10.152: 0.02777777777777777623: 0.0555555555555555534: 0.0833333333333333345: 0.111111111111111156: 0.138888888888888967: 0.1666666666666666678: 0.138888888888888989: 0.1111111111111111910: 0.083333333333333331011: 0.055555555555555551112: 0.02777777777777777612
Probability of each total with 2 dice of 6 sides; highlighted bars make up the answer.
Step-by-step working (3 steps)

  1. Count all outcomes

    Each die has 6 faces, so there are 6^2 equally likely outcomes.

    62=366^{2} = 36

  2. Count favourable outcomes

    Build up the number of ways to make each total one die at a time.

    66

  3. Divide

    Favourable ÷ total.

    636=16\frac{6}{36} = \frac{1}{6}
Formulas used
P=favourable outcomestotal outcomesP = \frac{\text{favourable outcomes}}{\text{total outcomes}}
How this was checked
  • ✓ The ways for every possible total add up to 6^2 = 36.

Frequently asked questions

What is the most likely total with two dice?

7. Six of the 36 outcomes add to 7, so the probability is 1/6.

What is the chance of at least 15 with three dice?

20 of the 216 outcomes, which is 5/54 or about 9.3%.

Why are middle totals more likely?

There are more combinations that add up to them; only one way makes 2 or 12 with two dice.

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