Dice Probability Calculator
Find the probability of rolling a target sum with a set of identical dice. Enter the number of dice, the sides per die, and the target total; the tool counts the favorable outcomes and divides by all possible outcomes.
What this calculator does
The Dice Probability Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Find the probability of rolling a target sum with a set of identical dice. Enter the number of dice, the sides per die, and the target total; the tool counts the favorable outcomes and divides by all possible outcomes. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Dice Probability Calculator
Roll several identical dice and this calculator finds how likely a particular total is. It counts the number of ways the dice can add up to your target sum using a dynamic-programming pass over the faces, then divides by the total number of equally likely outcomes, which is sides raised to the number of dice.
You can use between 1 and 10 dice, and each die needs at least 2 sides. Results include the favorable outcomes, the total outcomes, and the probability as a percentage.
Formula & Mathematical Calculation
Calculation Method
- Compute i++){ nx=[]
- Compute } total=pow(s,d), ways=dp[t]||0
Calculation Example
With 2 dice, 6 sides each, and a target sum of 7:
- Favorable outcomes = 6 (for example 1+6, 2+5, 3+4 and their reverses)
- Total outcomes = 6² = 36
- Probability = 6 / 36 = 16.6667%
The panel shows 6 favorable outcomes out of 36, a 16.6667% chance.
Key Benefits
- Counts exact ways to reach a target sum with a dynamic-programming pass, not an estimate
- Shows favorable outcomes, total outcomes, and the probability together so the fraction is transparent
- Handles between 1 and 10 dice with any number of sides from 2 upward
- Reports the probability as a percentage to four decimals; free and in-browser
How to Use this Calculator
-
Enter the number of dice
Type how many dice you are rolling into Number of dice; between 1 and 10. -
Enter the sides per die
Type how many sides each die has into Sides per die; at least 2. -
Enter the target sum
Type the total you want the dice to add up to into Target sum. -
Calculate
Press Calculate to read the Favorable Outcomes, Total Outcomes, and Probability.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Dice Probability Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.