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Dice Probability Calculator
This is a probability calculator, not a random dice roller: it tells you exactly how likely a result is. Choose how many dice and how many sides, then a target total, to get the chance of rolling exactly, at least or at most that total — with the odds, the average roll and a table of every possible total.
- Odds
- 1 in 6
- Ways to roll it
- 6
- Possible outcomes
- 36
- Average total (expected value)
- 7
- Most likely total
- 7
- Possible totals
- 2 to 12
Chance of every total
| Total | Exactly | At least | At most |
|---|
Saved setups
Save a set of inputs you reuse — your usual rate, your loan, your room sizes — and load it back in one tap.
Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the number of dice, from 1 to 10.
- Choose the type of die, from d4 to d100.
- Choose exactly, at least or at most, and enter the target total.
- Read the probability and odds, and scroll the table to see every total.
Worked examples
Rolling exactly 7 with two six-sided dice (6 of the 36 combinations)
- Ways to roll it
- 6
- Possible outcomes
- 36
- Probability
- 16.67%
- Odds
- 1 in 6
- Average total (expected value)
- 7
- Most likely total
- 7
Rolling 15 or more with three six-sided dice (10 + 6 + 3 + 1 = 20 of 216 combinations)
- Ways to roll it
- 20
- Possible outcomes
- 216
- Probability
- 9.26%
- Odds
- 1 in 10.8
- Average total (expected value)
- 10.5
- Most likely total
- 10 and 11
Rolling 15 or higher on a d20 (6 of 20 faces)
- Ways to roll it
- 6
- Probability
- 30%
- Odds
- 1 in 3.3
- Average total (expected value)
- 10.5
Two six-sided dice
There are 36 equally likely combinations. Seven is the most likely total because six of them make it (1+6, 2+5, 3+4 and their reverses): 16.67%. The chances fall away evenly on each side: 6 and 8 are 13.89% each, 5 and 9 are 11.11%, 4 and 10 are 8.33%, 3 and 11 are 5.56%, and 2 and 12 are 2.78% each — one combination out of 36.
More dice, more bell-shaped
One die gives every face the same chance. Add dice and the totals bunch up around the average, because there are many more ways to make a middling total than an extreme one. With 3d6, a total of 10 or 11 comes up 12.5% of the time each, while 3 or 18 comes up only 0.46% of the time — once in 216 rolls.
That is why games use several dice when they want consistent results and a single d20 when they want swingy ones: on a d20, every number from 1 to 20 has the same 5% chance.
Dice have no memory
Each roll is independent. Rolling three sixes in a row does not make a fourth less likely — it is still 1 in 6. The probabilities here describe what happens over many rolls of fair dice, not what the next roll “owes” you.
Questions people ask
What is the probability of rolling a 7 with two dice?
6 in 36, which is 16.67% or 1 in 6. It is the most likely total with two six-sided dice.
What are the odds of rolling a 12 with two dice?
1 in 36, or 2.78%. Only a double six makes 12.
What is the chance of rolling a 20 on a d20?
5%, or 1 in 20. Rolling 15 or higher is 30%.
What is the average roll of 3d6?
10.5. Each six-sided die averages 3.5, and averages add up.