A dice probability calculator with exact odds
What are the chances of rolling at least 15 on a d20 with a +5 bonus? With advantage? Of rolling 7 on two dice, or 18 on 4d6 drop the lowest? This dice probability calculator answers these exactly. Type any dice expression, pick at least, at most, exactly or between and a target, and it shows the probability as a percentage, as an exact fraction and as “1 in N”, with a graph of every possible total.
It handles modifiers, advantage and disadvantage, keep and drop rules, rerolls (Great Weapon Fighting style), Fudge dice and dice pools that count successes against a target number. Every result is calculated exactly, not simulated, so 1 in 216 really is 1 in 216. Nothing is uploaded; the arithmetic runs in your browser.
How to use the Dice Probability Calculator
- Type a dice expression such as
3d6+2,2d20kh1+5or6d10>7, or tap one of the examples. - Choose whether you want the chance of a total that is at least, at most, exactly, or between two numbers.
- Enter the target — for a d20 check, the DC or armour class you need to meet.
- Read the percentage, the exact fraction, the average, standard deviation and most likely total, and look at the graph: the highlighted bars are the outcomes you asked about.
- Open the probability table for every total, then copy the result or download the table as CSV.
Dice Probability Calculator features
Exact fractions
Counts are kept as whole numbers over a common denominator, so even 100d6 is exact; the percentage is rounded only for display.
Advantage and keep/drop
kh, kl, dh and dl use an exact order-statistics method, so 2d20kh1 and 4d6dl1 are right, not estimated.
Rerolls
ro<2 rerolls 1s and 2s once and keeps the new roll; r<1 rerolls until the die beats 1.
Dice pools
6d10>7 counts dice that roll 8 or more, for World of Darkness, Shadowrun-style and other success-counting systems.
Graph and table
A bar chart of the whole distribution, and a table of exactly, at least and at most for every total.
How the probabilities are calculated
Each die is a list of equally likely faces. The distribution of a sum is found by convolution: the chance of each total of two dice is the sum, over every way of making it, of the product of the individual chances. Repeating this gives any number of dice; flat modifiers just shift the result and a subtracted die is mirrored. The probability of “at least 15” is the sum of the chances of 15 and every higher total.
Keep-highest and drop-lowest rolls cannot be found by simple convolution, so the calculator walks through the face values from the top (or bottom), counting with binomial coefficients how many dice show each value and how many are kept. A reroll-once rule changes each face’s weight: on a d6 with ro<2, a 6 can come up directly (1/6) or after a reroll (2/6 × 1/6), so it has weight 8/36.
| Roll | Question | Exact | Percent |
|---|---|---|---|
| 2d6 | exactly 7 | 1/6 | 16.67% |
| 3d6 | at least 18 | 1/216 | 0.46% |
| 1d20+5 | at least 15 | 11/20 | 55% |
| 2d20kh1+5 (advantage) | at least 15 | 319/400 | 79.75% |
| 2d20kl1+5 (disadvantage) | at least 15 | 121/400 | 30.25% |
| 4d6dl1 | exactly 18 | 7/432 | 1.62% |
Advantage, disadvantage and modifiers
With advantage you roll two d20 and keep the higher, so you miss only if both dice miss: the chance of success is 1 − (miss chance)². Against a target that a single d20 hits 55% of the time, advantage raises it to 79.75%; disadvantage (both must hit) drops it to 30.25%. The boost is largest for middling targets — about +25 percentage points when you need an 11 — and small at the extremes.
A modifier moves the whole distribution without changing its shape: 1d20+5 against 15 is the same as a plain d20 against 10. To roll the dice instead of studying them, use the dice roller; for coins, cards and other events, the probability calculator covers combinations and repeated trials.
Dice Probability Calculator FAQ
How do I calculate dice probability?
Count the outcomes that meet your condition and divide by all possible outcomes. Two dice have 36 outcomes and six of them total 7, so the chance is 6/36 = 1/6. The dice probability calculator does this exactly for any expression.
What is the probability of rolling a 7 with two dice?
1/6, about 16.67%. Seven is the most likely total of 2d6 because it can be made in six ways.
How much does advantage help?
It turns a success chance p into 1 − (1 − p)². A 50% roll becomes 75%, and a natural 20 goes from 5% to 9.75%.
Can it handle modifiers and several kinds of dice?
Yes. Join terms with + or −, for example 1d8+2d6+3 or 1d20+1d4+5. A subtracted die such as 1d6−1d4 is handled exactly.
Why are exploding dice not supported?
An exploding die rolls again on its highest face, so totals have no upper limit and there is no finite exact table. Remove the “!” to get the odds without explosions.
How do dice pools with target numbers work?
Write the pool with a threshold, such as 6d10>7 for “count dice showing 8 or more”. The result is the distribution of the number of successes, and “at least 3” gives the chance of 3 or more.