Dice sum probability calculator

Calculate probability with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use probability to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Dice
2
Sides per die
6
Target sum
7
Probability
0.166667

Try another scenario

Dice
3
Sides per die
6
Target sum
7
Probability
0.069444
Calculation method

Calculation method

Probability

diceTotalProbability(a,b,c)

Symbols and units
a
Dice
b
Sides per die
c
Target sum

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Calculation steps and notation

Build counts of attainable sums one die at a time. For each previous sum, add its count to the sums formed by each face 1 through s. Probability = the target sum’s count divided by s^n for n dice.

Assumptions & limits

Assumptions & limits

  • Fair independent dice with faces numbered from one. Uses an exact count distribution within supported limits.
Are these inputs private?

These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.

Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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