Calculate fair-dice sum and chosen-face event probabilities with convolution or binomial counting, including exact and cumulative events.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Sum probabilities use repeated convolution of fair face probabilities. Chosen-face counts use a binomial distribution with p=1/s.
Assumptions and limits
Identical independent fair dice numbered 1 through s. Up to 30 dice and 100 sides, with bounded computation. No special game mechanics or weighted faces.
Worked example
Two fair six-sided dice have 36 equally likely ordered face pairs. Six pairs total 7, so P(sum = 7) = 1/6. Twenty-one pairs total at least 7, giving 21/36. A different event, at least one six on three dice, has probability 1−(5/6)³ = 91/216. Select the event before entering its target: a target sum and a selected face mean different things.
Worked reading and practical questions
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Identical independent fair dice numbered 1 through s. Up to 30 dice and 100 sides, with bounded computation. No special game mechanics or weighted faces.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.