The four-sided die is a tetrahedron, the simplest regular solid: four triangular faces and four points. Because it has no face pointing straight up, the result is read either from the number printed along the bottom edges or at the top vertex, depending on how the die is made. It also cannot roll far, which is why players often shake it in the hand or a cup.
In role-playing games the d4 is the small-damage die – daggers, magic missiles and minor healing potions – and several d4s are often rolled together, as in 2d4 + 2. Each face has exactly a 25% chance, the average of one die is 2.5 and the total of several d4s quickly clusters around its average: 3d4 lands on 7 or 8 almost 38% of the time.
This roller throws up to 100 d4s with a secure random generator, adds your modifier, lists each die, counts the faces and draws the exact distribution of the total with your roll highlighted, so you can see whether that 3 on 3d4 was as unlucky as it felt (it was: 1 in 64).
How to use the 4-Sided Dice Roller
- Number of d4s
- Modifier added to the total
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Each die is a uniform random integer from 1 to 4. The probability of every total is calculated exactly by convolving the dice.
Worked example
Rolling 3d4 gave 2, 4 and 1: a total of 7. The expected total is 3 × 2.5 = 7.5 and totals run from 3 to 12. A total of 7 can be made 12 ways out of 4³ = 64, a chance of 18.75% – tied with 8 as the most likely total.
Totals of 2d4
| Total | Ways | Probability |
|---|---|---|
| 2 | 1 | 6.25% |
| 3 | 2 | 12.5% |
| 4 | 3 | 18.75% |
| 5 | 4 | 25% |
| 6 | 3 | 18.75% |
| 7 | 2 | 12.5% |
| 8 | 1 | 6.25% |
Formula
One d4: P(any face) = 1/4 = 25% · average 2.5 · n d4: average 2.5n, variance 1.25n
Worked example
Inputs — Number of d4s: 1; Modifier added to the total: 0.
Results — Total = 1; Individual dice = 1; Average (expected) total = 2.5; Possible totals = 1 to 4; Chance of rolling exactly this total = 25 %.
Key terms
- d4
- A four-sided die shaped like a tetrahedron.
- Tetrahedron
- A solid with four triangular faces, the shape of the d4.
- Modifier
- A fixed bonus or penalty added to a roll.
Frequently asked questions
What is the average roll of a d4?
2.5, the mean of 1, 2, 3 and 4.
How do you read a d4?
Look for the number that is upright at the top point, or along the bottom edges on dice printed that way; the same number appears on all three visible faces.
What is the chance of rolling a 4 on a d4?
1 in 4, or 25%.
What is the average of 2d4 + 2?
2 × 2.5 + 2 = 7, with totals from 4 to 10.
What is the chance of rolling all 1s on 3d4?
(1/4)³ = 1/64 ≈ 1.56%.
What is a d4 used for in D&D?
Dagger and club damage, Magic Missile (1d4 + 1 per dart), the Bless and Guidance bonuses and small healing potions (2d4 + 2).