Dice sum probability distribution
Compare the chance of an exact sum with the chance of reaching or exceeding it using fair independent dice.
Your inputs
Start with the example values, then replace them with your own. For tables, keep the vertical bar separators and use a dot for decimals.
This educational model assumes fair, independent dice. Probabilities are calculated by combining distributions, not by random trials. The results do not predict an individual roll; do not use them for gambling decisions.
Tool inputs are processed in your browser and are not submitted by this tool. Existing site analytics and advertising services have their own privacy terms.
Result and workspace
Use the start button to open your result or activity.
How it works
Repeated convolution combines the uniform distribution of each die. Probabilities assume fair, independent dice; this is an educational model, not a gambling recommendation.
Worked example
These sample results use the original example inputs in the form. They do not change when you edit your inputs; your own result appears in the workspace.
- Exact probability: 11.5741 %
- At least probability: 37.5 %
| Sum | Probability (%) |
|---|---|
| 3 | 0.463 |
| 4 | 1.3889 |
| 5 | 2.7778 |
| 6 | 4.6296 |
Read the result carefully
Results depend on the values and assumptions shown above. Change one input at a time to see its effect. A blank or unavailable result means the data does not support a calculation; it is not zero.