4-Sided Dice Roller Calculator
Roll one or more four-sided dice (D4) and get your total plus individual die results in a single click. Set a modifier to add or subtract a flat bonus, choose how many dice to roll, and see the theoretical mean, minimum, and maximum for your combination. The probability breakdown and reference table explain exactly how likely each total is before you roll.
What is a D4 and how does it work?
A D4 is a four-sided die in the shape of a tetrahedron, a pyramid with four equilateral triangular faces. Unlike a standard six-sided die, a D4 does not have a flat face pointing upward when it lands. Instead, the result is usually read from the face pointing down or from the number printed at the apex. Because there are four equal faces, every outcome from 1 to 4 has exactly a 1-in-4 (25%) chance on each roll. D4 dice have been used for games and divination since ancient times, predating the six-sided die in some cultures. In modern tabletop RPGs such as Dungeons and Dragons, the D4 is used for small damage rolls (daggers, magic missile), minor healing, and random tables with four options.
How to use this calculator
Set the number of dice (1 to 10), enter a modifier if your game rules add or subtract a flat bonus (for example +3 from a Strength ability modifier), and choose a roll mode. Standard mode sums all dice. Drop-lowest rolls all the dice and discards the single smallest result before summing, which is useful for generating ability scores or advantage-style rolls. Keep-highest keeps only the single best die from however many you rolled, effectively giving you advantage on a single die. Toggle the roll input or change any setting to generate a fresh set of random results. The probability chart below the result shows you exactly how likely each total is before you commit.
Probability and the law of averages
A single D4 has a flat (uniform) distribution: every value from 1 to 4 is equally likely at 25%. When you roll multiple D4 dice and sum them, the distribution becomes a discrete convolution of uniform distributions. With two dice the possible sums range from 2 to 8, but the middle values (4, 5 and 6) are more likely than the extremes because there are more ways to make them. With more dice the distribution approaches a bell curve centred on the mean (N x 2.5, where N is the number of dice). The probability chart on this page shows the exact distribution for your chosen settings so you can see at a glance whether you need a high roll and what your realistic chances are.
Modifiers and roll modes
In most RPG systems a flat modifier is added or subtracted after the roll. For example, a Strength score of 16 gives a +3 modifier in D&D 5e, so a dagger dealing 1D4+3 would produce results of 4 to 7. Drop-lowest is most commonly used when rolling 4D6 to generate ability scores: you roll four dice and drop the lowest, then sum the remaining three for a score between 3 and 18. Keep-highest is similar to advantage: rolling two dice and keeping the larger skews the distribution upward. This calculator handles all three modes and updates the probability chart accordingly.
D4 probability reference by number of dice
| Dice (N) | Min | Max | Mean | Most common total |
|---|---|---|---|---|
| 1 | 1 | 4 | 2.50 | 1, 2, 3 or 4 (equal 25%) |
| 2 | 2 | 8 | 5.00 | 5 (11.1%) |
| 3 | 3 | 12 | 7.50 | 7 or 8 (12.5%) |
| 4 | 4 | 16 | 10.00 | 10 (11.7%) |
| 5 | 5 | 20 | 12.50 | 12 or 13 (11.5%) |
| 6 | 6 | 24 | 15.00 | 15 (10.5%) |
Theoretical statistics for rolling N standard D4 dice with no modifier in standard mode.
Frequently asked questions
What weapons or spells use a D4 in Dungeons and Dragons?
In D&D 5e, weapons that deal D4 damage include the dagger, handaxe (improvised), and many cantrips and low-level spells. The spell Magic Missile deals 1D4+1 force damage per missile, Healing Word restores 1D4 plus a spellcasting modifier, and Bless adds 1D4 to attack rolls and saving throws. The D4 is also the damage die for the dart and the torch used as an improvised weapon.
What is the average roll on a single D4?
The theoretical average is 2.5 (the sum of all faces 1+2+3+4 = 10, divided by 4 faces = 2.5). Because 2.5 is not a whole number, you will never roll exactly the average on a single die, but over many rolls the mean converges to 2.5. For two D4 dice, the mean is 5.0, and for N dice it is N x 2.5.
What is the probability of rolling a 4 on a D4?
Exactly 25% (1 in 4) for a single fair die. Rolling at least one 4 on two dice is 1 minus the probability of rolling no 4s, which is 1 - (3/4)^2 = 7/16 = 43.75%. For three dice the probability of at least one 4 is 1 - (3/4)^3 = 37/64 = 57.8%.
How does drop-lowest change the average?
Dropping the lowest die of N raises the average because you are always removing a below-average result. For 2D4 drop lowest (common in some bonus calculations), the mean rises from 5.0 to about 3.125 on a single surviving die (roughly 3.1). For 4D6 drop lowest, the average sum of the remaining three dice is about 12.24 instead of 10.5 for a straight 3D6.
How is a D4 different from other polyhedral dice?
A D4 is a tetrahedron with 4 faces. The other standard RPG dice are: D6 (cube, 6 faces), D8 (octahedron, 8 faces), D10 (pentagonal trapezohedron, 10 faces), D12 (dodecahedron, 12 faces), and D20 (icosahedron, 20 faces). The D4 produces the smallest non-trivial range of values and has the flattest distribution of any standard polyhedral die used in tabletop gaming.
Are virtual dice rolls truly random?
Virtual dice use a pseudo-random number generator (PRNG). Modern PRNGs such as the Mersenne Twister or cryptographic generators are statistically indistinguishable from true randomness for game purposes and are often more uniform than mass-produced physical dice, which can have slight imbalances due to manufacturing tolerances. For casual play and probability study, virtual dice are perfectly suitable.