Dice Sum Probability Calculator
Count exact outcomes for the sum of fair dice. Choose an exact sum, a tail or an inclusive range and inspect the entire distribution.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Build the sum counts one die at a time. Every existing partial sum branches to faces1 throughs. Add the selected sum counts and divide bys^n equally likely ordered rolls.
P(event)=selected ordered rolls / sides^dice
Worked example
Two six-sided dice have36 ordered rolls. Sum7 occurs in6 ways, so its probability is1/6. Sums are not equally likely.
Assumptions and input details
Dice must be independent and fair, with the same number of sides labelled1 throughs. Up to10 dice with2–20 sides are supported. Targets are integers within±1000; impossible sums have probability0. Counts and fractions are exact. Charts and percentage displays are rounded.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Outcome counts and probability fractions are exact. Percentages and the chart are rounded.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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