Probabilities of Sums on Various Numbers of D6 Dice

Table of Contents
Terms
  • Result: The sum of all rolled dice.
  • Fraction: Chance of getting that exact result expressed as a fraction.
  • Percent: Chance of getting that exact result expressed as a precentage.
  • Cumulative Fraction: Chance of getting equal to or less than that result expressed as a fraction.
  • Cumulative Percent: Chance of getting equal to or less than that result expressed as a percentage.
1d6
Result Fraction Percent Cumulative
Fraction		 Cumulative
Percent		 Notes
1 1/6 16.6% 1/6 16.6%
2 1/6 16.6% 2/6 33.3%
3 1/6 16.6% 3/6 50%
4 1/6 16.6% 4/6 66.6%
5 1/6 16.6% 5/6 83.3%
6 1/6 16.6% 6/6 100%

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2d6
Result Fraction Percent Cumulative
Fraction		 Cumulative
Percent		 Notes
2 1/36 2.8% 1/36 2.8%
3 2/36 5.6% 3/36 8.3%
4 3/36 8.3% 6/36 16.7%
5 4/36 11.1% 10/36 27.8%
6 5/36 13.9% 15/36 41.7%
7 6/36 16.7% 21/36 58.3%
8 5/36 13.9% 26/36 72.2%
9 4/36 11.1% 30/36 83.3%
10 3/36 8.3% 33/36 91.7%
11 2/36 5.6% 35/36 97.2%
12 1/36 2.8% 36/36 100%

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3d6
Result Fraction Percent Cumulative
Fraction		 Cumulative
Percent		 Notes
3 1/216 0.5% 1/216 0.5%
4 3/216 1.4% 4/216 1.9%
5 6/216 2.8% 10/216 4.6%
6 10/216 4.6% 20/216 9.3%
7 15/216 6.9% 35/216 16.2%
8 21/216 9.7% 56/216 25.9%
9 25/216 11.6% 81/216 37.5%
10 27/216 12.5% 108/216 50%
11 27/216 12.5% 135/216 62.5%
12 25/216 11.6% 160/216 74.1%
13 21/216 9.7% 181/216 83.8%
14 15/216 6.9% 196/216 90.7%
15 10/216 4.6% 206/216 95.4%
16 6/216 2.8% 212/216 98.1%
17 3/216 1.4% 215/216 99.5%
18 1/216 0.5% 216/216 100%

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Result Fraction Percent Cumulative
Fraction		 Cumulative
Percent		 Notes
% %
% %
% %

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