What is a D20 Dice Roller?
A d20 is a twenty-sided die, the iconic die of Dungeons & Dragons and countless other tabletop role-playing games. This calculator simulates rolling one or more virtual d20 dice and adds an optional modifier to the total — perfect for attack rolls, ability checks, and saving throws when you don't have physical dice on hand.
How to use it
Enter how many d20 dice you want to roll (1 to 100) and an optional modifier such as +5 or -2. Press calculate and you'll get the combined total, the raw dice subtotal, the modifier applied, plus the highest and lowest single roll in the batch. Refresh or re-submit to roll again.
The formula explained
Each die uses roll = floor(random() × 20) + 1. A random fraction between 0 and 1 is scaled to the range 0–19.999, floored to a whole number 0–19, then shifted by 1 to give an integer from 1 to 20 with equal probability. The grand total is the sum of every die plus your modifier.
$$\text{Total} = \sum_{i=1}^{\text{Number of d20}} \left(\lfloor \text{rand} \times 20 \rfloor + 1\right) + \text{Modifier}$$
Worked example
Suppose you roll 2d20 and the dice land on 14 and 7 with a +3 modifier. The dice subtotal is \(14 + 7 = 21\), and the grand total is \(21 + 3 = 24\). The highest single roll is 14 and the lowest is 7.
FAQ
Are the rolls truly random? They use a pseudo-random number generator that produces a uniform, fair distribution across 1–20 for typical gaming use.
Can I roll a natural 20? Yes — any single die can return 20 (a "crit") or 1 (a "fumble"), shown in the highest and lowest rows.
Why do I get a new result each time? Every submission re-rolls the dice, so totals change between rolls just like real dice.
