Dice sum odds — all 111 outcomes
Every sum you can roll with one to six ordinary dice, with the number of ways it happens and how likely it is. Handy when you want to know what a board game roll will really give you.
One die6
6 equally likely rolls, with sums from 1 to 6.
2 dice11
36 equally likely rolls, with sums from 2 to 12.
3 dice16
216 equally likely rolls, with sums from 3 to 18.
30.46%Ways to roll it 141.39%Ways to roll it 352.78%Ways to roll it 664.63%Ways to roll it 1076.94%Ways to roll it 1589.72%Ways to roll it 21911.57%Ways to roll it 251012.5%Ways to roll it 27 · Most likely sum1112.5%Ways to roll it 27 · Most likely sum1211.57%Ways to roll it 25139.72%Ways to roll it 21146.94%Ways to roll it 15154.63%Ways to roll it 10162.78%Ways to roll it 6171.39%Ways to roll it 3180.46%Ways to roll it 1
4 dice21
1,296 equally likely rolls, with sums from 4 to 24.
40.08%Ways to roll it 150.31%Ways to roll it 460.77%Ways to roll it 1071.54%Ways to roll it 2082.7%Ways to roll it 3594.32%Ways to roll it 56106.17%Ways to roll it 80118.02%Ways to roll it 104129.65%Ways to roll it 1251310.8%Ways to roll it 1401411.27%Ways to roll it 146 · Most likely sum1510.8%Ways to roll it 140169.65%Ways to roll it 125178.02%Ways to roll it 104186.17%Ways to roll it 80194.32%Ways to roll it 56202.7%Ways to roll it 35211.54%Ways to roll it 20220.77%Ways to roll it 10230.31%Ways to roll it 4240.08%Ways to roll it 1
5 dice26
7,776 equally likely rolls, with sums from 5 to 30.
50.01%Ways to roll it 160.06%Ways to roll it 570.19%Ways to roll it 1580.45%Ways to roll it 3590.9%Ways to roll it 70101.62%Ways to roll it 126112.64%Ways to roll it 205123.92%Ways to roll it 305135.4%Ways to roll it 420146.94%Ways to roll it 540158.37%Ways to roll it 651169.45%Ways to roll it 7351710.03%Ways to roll it 780 · Most likely sum1810.03%Ways to roll it 780 · Most likely sum199.45%Ways to roll it 735208.37%Ways to roll it 651216.94%Ways to roll it 540225.4%Ways to roll it 420233.92%Ways to roll it 305242.64%Ways to roll it 205251.62%Ways to roll it 126260.9%Ways to roll it 70270.45%Ways to roll it 35280.19%Ways to roll it 15290.06%Ways to roll it 5300.01%Ways to roll it 1
6 dice31
46,656 equally likely rolls, with sums from 6 to 36.
60.0021%Ways to roll it 170.01%Ways to roll it 680.05%Ways to roll it 2190.12%Ways to roll it 56100.27%Ways to roll it 126110.54%Ways to roll it 252120.98%Ways to roll it 456131.62%Ways to roll it 756142.49%Ways to roll it 1,161153.57%Ways to roll it 1,666164.82%Ways to roll it 2,247176.12%Ways to roll it 2,856187.35%Ways to roll it 3,431198.37%Ways to roll it 3,906209.05%Ways to roll it 4,221219.28%Ways to roll it 4,332 · Most likely sum229.05%Ways to roll it 4,221238.37%Ways to roll it 3,906247.35%Ways to roll it 3,431256.12%Ways to roll it 2,856264.82%Ways to roll it 2,247273.57%Ways to roll it 1,666282.49%Ways to roll it 1,161291.62%Ways to roll it 756300.98%Ways to roll it 456310.54%Ways to roll it 252320.27%Ways to roll it 126330.12%Ways to roll it 56340.05%Ways to roll it 21350.01%Ways to roll it 6360.0021%Ways to roll it 1
7 dice36
279,936 equally likely rolls, with sums from 7 to 42.
70.00036%Ways to roll it 180.0025%Ways to roll it 790.01%Ways to roll it 28100.03%Ways to roll it 84110.08%Ways to roll it 210120.17%Ways to roll it 462130.33%Ways to roll it 917140.6%Ways to roll it 1,667151%Ways to roll it 2,807161.58%Ways to roll it 4,417172.34%Ways to roll it 6,538183.27%Ways to roll it 9,142194.33%Ways to roll it 12,117205.45%Ways to roll it 15,267216.55%Ways to roll it 18,327227.5%Ways to roll it 20,993238.2%Ways to roll it 22,967248.58%Ways to roll it 24,017 · Most likely sum258.58%Ways to roll it 24,017 · Most likely sum268.2%Ways to roll it 22,967277.5%Ways to roll it 20,993286.55%Ways to roll it 18,327295.45%Ways to roll it 15,267304.33%Ways to roll it 12,117313.27%Ways to roll it 9,142322.34%Ways to roll it 6,538331.58%Ways to roll it 4,417341%Ways to roll it 2,807350.6%Ways to roll it 1,667360.33%Ways to roll it 917370.17%Ways to roll it 462380.08%Ways to roll it 210390.03%Ways to roll it 84400.01%Ways to roll it 28410.0025%Ways to roll it 7420.00036%Ways to roll it 1
8 dice41
1,679,616 equally likely rolls, with sums from 8 to 48.
80.00006%Ways to roll it 190.00048%Ways to roll it 8100.0021%Ways to roll it 36110.01%Ways to roll it 120120.02%Ways to roll it 330130.05%Ways to roll it 792140.1%Ways to roll it 1,708150.2%Ways to roll it 3,368160.37%Ways to roll it 6,147170.62%Ways to roll it 10,480181%Ways to roll it 16,808191.52%Ways to roll it 25,488202.18%Ways to roll it 36,688212.99%Ways to roll it 50,288223.92%Ways to roll it 65,808234.9%Ways to roll it 82,384245.88%Ways to roll it 98,813256.77%Ways to roll it 113,688267.48%Ways to roll it 125,588277.94%Ways to roll it 133,288288.09%Ways to roll it 135,954 · Most likely sum297.94%Ways to roll it 133,288307.48%Ways to roll it 125,588316.77%Ways to roll it 113,688325.88%Ways to roll it 98,813334.9%Ways to roll it 82,384343.92%Ways to roll it 65,808352.99%Ways to roll it 50,288362.18%Ways to roll it 36,688371.52%Ways to roll it 25,488381%Ways to roll it 16,808390.62%Ways to roll it 10,480400.37%Ways to roll it 6,147410.2%Ways to roll it 3,368420.1%Ways to roll it 1,708430.05%Ways to roll it 792440.02%Ways to roll it 330450.01%Ways to roll it 120460.0021%Ways to roll it 36470.00048%Ways to roll it 8480.00006%Ways to roll it 1
9 dice46
10,077,696 equally likely rolls, with sums from 9 to 54.
90.00001%Ways to roll it 1100.000089%Ways to roll it 9110.00045%Ways to roll it 45120.0016%Ways to roll it 165130.0049%Ways to roll it 495140.01%Ways to roll it 1,287150.03%Ways to roll it 2,994160.06%Ways to roll it 6,354170.12%Ways to roll it 12,465180.23%Ways to roll it 22,825190.39%Ways to roll it 39,303200.64%Ways to roll it 63,999210.98%Ways to roll it 98,979221.45%Ways to roll it 145,899232.04%Ways to roll it 205,560242.75%Ways to roll it 277,464253.57%Ways to roll it 359,469264.44%Ways to roll it 447,669275.32%Ways to roll it 536,569286.15%Ways to roll it 619,569296.84%Ways to roll it 689,715307.35%Ways to roll it 740,619317.61%Ways to roll it 767,394 · Most likely sum327.61%Ways to roll it 767,394 · Most likely sum337.35%Ways to roll it 740,619346.84%Ways to roll it 689,715356.15%Ways to roll it 619,569365.32%Ways to roll it 536,569374.44%Ways to roll it 447,669383.57%Ways to roll it 359,469392.75%Ways to roll it 277,464402.04%Ways to roll it 205,560411.45%Ways to roll it 145,899420.98%Ways to roll it 98,979430.64%Ways to roll it 63,999440.39%Ways to roll it 39,303450.23%Ways to roll it 22,825460.12%Ways to roll it 12,465470.06%Ways to roll it 6,354480.03%Ways to roll it 2,994490.01%Ways to roll it 1,287500.0049%Ways to roll it 495510.0016%Ways to roll it 165520.00045%Ways to roll it 45530.000089%Ways to roll it 9540.00001%Ways to roll it 1
10 dice51
60,466,176 equally likely rolls, with sums from 10 to 60.
100.000002%Ways to roll it 1110.000017%Ways to roll it 10120.000091%Ways to roll it 55130.00036%Ways to roll it 220140.0012%Ways to roll it 715150.0033%Ways to roll it 2,002160.01%Ways to roll it 4,995170.02%Ways to roll it 11,340180.04%Ways to roll it 23,760190.08%Ways to roll it 46,420200.14%Ways to roll it 85,228210.24%Ways to roll it 147,940220.4%Ways to roll it 243,925230.63%Ways to roll it 383,470240.95%Ways to roll it 576,565251.37%Ways to roll it 831,204261.9%Ways to roll it 1,151,370272.54%Ways to roll it 1,535,040283.26%Ways to roll it 1,972,630294.05%Ways to roll it 2,446,300304.85%Ways to roll it 2,930,455315.61%Ways to roll it 3,393,610326.29%Ways to roll it 3,801,535336.82%Ways to roll it 4,121,260347.15%Ways to roll it 4,325,310357.27%Ways to roll it 4,395,456 · Most likely sum367.15%Ways to roll it 4,325,310376.82%Ways to roll it 4,121,260386.29%Ways to roll it 3,801,535395.61%Ways to roll it 3,393,610404.85%Ways to roll it 2,930,455414.05%Ways to roll it 2,446,300423.26%Ways to roll it 1,972,630432.54%Ways to roll it 1,535,040441.9%Ways to roll it 1,151,370451.37%Ways to roll it 831,204460.95%Ways to roll it 576,565470.63%Ways to roll it 383,470480.4%Ways to roll it 243,925490.24%Ways to roll it 147,940500.14%Ways to roll it 85,228510.08%Ways to roll it 46,420520.04%Ways to roll it 23,760530.02%Ways to roll it 11,340540.01%Ways to roll it 4,995550.0033%Ways to roll it 2,002560.0012%Ways to roll it 715570.00036%Ways to roll it 220580.000091%Ways to roll it 55590.000017%Ways to roll it 10600.000002%Ways to roll it 1
11 dice56
362,797,056 equally likely rolls, with sums from 11 to 66.
110%Ways to roll it 1120.000003%Ways to roll it 11130.000018%Ways to roll it 66140.000079%Ways to roll it 286150.00028%Ways to roll it 1,001160.00083%Ways to roll it 3,003170.0022%Ways to roll it 7,997180.01%Ways to roll it 19,327190.01%Ways to roll it 43,032200.02%Ways to roll it 89,232210.05%Ways to roll it 173,745220.09%Ways to roll it 319,683230.15%Ways to roll it 558,613240.26%Ways to roll it 930,743250.41%Ways to roll it 1,483,548260.63%Ways to roll it 2,268,332270.92%Ways to roll it 3,334,474281.3%Ways to roll it 4,721,574291.78%Ways to roll it 6,450,279302.35%Ways to roll it 8,513,109313%Ways to roll it 10,866,999323.7%Ways to roll it 13,429,405334.43%Ways to roll it 16,079,570345.14%Ways to roll it 18,665,790355.79%Ways to roll it 21,018,470366.33%Ways to roll it 22,967,626376.72%Ways to roll it 24,362,481386.92%Ways to roll it 25,090,131 · Most likely sum396.92%Ways to roll it 25,090,131 · Most likely sum406.72%Ways to roll it 24,362,481416.33%Ways to roll it 22,967,626425.79%Ways to roll it 21,018,470435.14%Ways to roll it 18,665,790444.43%Ways to roll it 16,079,570453.7%Ways to roll it 13,429,405463%Ways to roll it 10,866,999472.35%Ways to roll it 8,513,109481.78%Ways to roll it 6,450,279491.3%Ways to roll it 4,721,574500.92%Ways to roll it 3,334,474510.63%Ways to roll it 2,268,332520.41%Ways to roll it 1,483,548530.26%Ways to roll it 930,743540.15%Ways to roll it 558,613550.09%Ways to roll it 319,683560.05%Ways to roll it 173,745570.02%Ways to roll it 89,232580.01%Ways to roll it 43,032590.01%Ways to roll it 19,327600.0022%Ways to roll it 7,997610.00083%Ways to roll it 3,003620.00028%Ways to roll it 1,001630.000079%Ways to roll it 286640.000018%Ways to roll it 66650.000003%Ways to roll it 11660%Ways to roll it 1
12 dice61
2,176,782,336 equally likely rolls, with sums from 12 to 72.
120%Ways to roll it 1130.000001%Ways to roll it 12140.000004%Ways to roll it 78150.000017%Ways to roll it 364160.000063%Ways to roll it 1,365170.0002%Ways to roll it 4,368180.00057%Ways to roll it 12,364190.0015%Ways to roll it 31,680200.0034%Ways to roll it 74,646210.01%Ways to roll it 163,592220.02%Ways to roll it 336,336230.03%Ways to roll it 653,016240.06%Ways to roll it 1,203,632250.1%Ways to roll it 2,115,048260.16%Ways to roll it 3,555,564270.26%Ways to roll it 5,734,664280.41%Ways to roll it 8,895,393290.61%Ways to roll it 13,297,284300.88%Ways to roll it 19,188,950311.23%Ways to roll it 26,771,316321.66%Ways to roll it 36,154,767332.17%Ways to roll it 47,315,840342.76%Ways to roll it 60,060,936353.4%Ways to roll it 74,005,152364.07%Ways to roll it 88,573,343374.73%Ways to roll it 103,027,860385.35%Ways to roll it 116,523,342395.89%Ways to roll it 128,184,068406.3%Ways to roll it 137,194,629416.56%Ways to roll it 142,891,320426.65%Ways to roll it 144,840,476 · Most likely sum436.56%Ways to roll it 142,891,320446.3%Ways to roll it 137,194,629455.89%Ways to roll it 128,184,068465.35%Ways to roll it 116,523,342474.73%Ways to roll it 103,027,860484.07%Ways to roll it 88,573,343493.4%Ways to roll it 74,005,152502.76%Ways to roll it 60,060,936512.17%Ways to roll it 47,315,840521.66%Ways to roll it 36,154,767531.23%Ways to roll it 26,771,316540.88%Ways to roll it 19,188,950550.61%Ways to roll it 13,297,284560.41%Ways to roll it 8,895,393570.26%Ways to roll it 5,734,664580.16%Ways to roll it 3,555,564590.1%Ways to roll it 2,115,048600.06%Ways to roll it 1,203,632610.03%Ways to roll it 653,016620.02%Ways to roll it 336,336630.01%Ways to roll it 163,592640.0034%Ways to roll it 74,646650.0015%Ways to roll it 31,680660.00057%Ways to roll it 12,364670.0002%Ways to roll it 4,368680.000063%Ways to roll it 1,365690.000017%Ways to roll it 364700.000004%Ways to roll it 78710.000001%Ways to roll it 12720%Ways to roll it 1
How to read this
- Two dice do not land evenly. There are six ways to make 7 and only one way to make 2.
- The more dice, the tighter the middle. With six dice almost everything lands near 21, while 6 or 36 turns up about once in 47,000 rolls.
- The average sum is 3.5 per die, because one die averages 3.5.
- Rare is not never — but nor is it due. Roll two dice thirty-six times and there is still roughly a 36% chance you never see a 2.
Frequently asked questions
QWhat are the odds of rolling a 7 with two dice?
Six of the thirty-six outcomes make 7, so 16.67% — one roll in six. It is built from 1+6, 2+5 and 3+4 each way round, which is why it is the most common total on two dice.
QWhy is one sum more likely than another?
Each die is fair, but the sums are not built from the same number of paths. There is one way to make 2 and six ways to make 7, and the sum with more paths comes up more often.
QIs a number that has not come up “due”?
No. Dice keep no memory of earlier rolls. After six 1s in a row, the chance of another 1 is still one in six.
QWhy do more dice bunch up in the middle?
High and low faces cancel each other out. Getting six 1s means six things going the same way at once, while thousands of different combinations add up to 21.
QHow were these numbers worked out?
Only the die count and the sum are stored. The distribution for one die is convolved with another die at a time to count the ways, and dividing by six to the power of the die count gives the probability.