5 Sided Dice Probability Calculator and d20 Odds

This 5 sided dice probability calculator works out the chance of rolling a target number or higher on a fair d20. Enter the target and the number of dice, then see the probability as both a fraction and a percentage.

Formula

For a fair 20-sided die with faces 1 through 20, the chance that one die reaches target T or higher is p = (21 − T) / 20, when T is between 1 and 20. For n independent dice, the chance of at least one success is P = 1 − (1 − p)ⁿ. The calculator also limits the result appropriately if the entered target is outside the die’s face range. T is the target face, n is the number of dice, and p and P are probabilities; the displayed outputs convert them to percent.

Worked Example

With the defaults, the target is 15 and the number of dice is 1. One die succeeds on 15, 16, 17, 18, 19, or 20: 6 faces out of 20, so p = 6/20 = 0.30. For one die, P = 1 − (1 − 0.30)¹ = 0.30. The calculator displays a 30.00% chance on at least one die and a 30.00% chance on one die.

When to Use a 5 Sided Dice Probability Calculator

Use it to estimate the odds of meeting a fixed d20 threshold, such as rolling 15 or higher. It can also show how rolling several independent dice changes the chance that at least one meets the target. This is useful for tabletop rules discussions, probability lessons, or checking a game mechanic; it does not decide what a particular game’s rule means.

The number of dice means separate rolls, each with its own result. The result is an “at least one” probability, not the chance that every die succeeds, the average roll, or the probability of getting exactly one success. For example, if you need all dice to reach the target, the relevant probability is p raised to the number of dice, which this calculator does not display.

How to Read the Result

A 30% result means that, over many repeated sets of rolls under the same assumptions, about 30 out of every 100 sets would include at least one qualifying die. It does not mean that a success is due after several failures: each fair roll remains independent. The single-die output helps compare the base chance with the multi-die result.

For a target of 20, only one face succeeds, so a single die has a 5% chance. A target of 1 or lower is met by every possible d20 result; a target above 20 cannot be met. The calculator’s expression handles those boundary cases by limiting the count of failing faces to the range from zero to 20.

Common Mistakes and Limits

Count successful faces inclusively: for a target of 15, the successful outcomes are 15 through 20, six outcomes, not five. Also distinguish “at least one” from “exactly one.” Rounding the displayed percentage can obscure small differences, so keep more precision when comparing close probabilities.

The calculation assumes a fair, standard d20 numbered 1 through 20 and independent rolls. It does not account for advantage rules, rerolls, modifiers, exploding dice, loaded dice, or a target altered by game-specific mechanics. Convert those rules into an equivalent probability model before relying on the result; a simple target alone cannot represent every dice mechanic.

Frequently Asked Questions

What is the chance of rolling a 20 on one d20?

One face out of 20 is a 20, so the chance is 1/20, or 5%, assuming a fair die.

What is the chance of rolling 15 or higher on a d20?

There are six successful faces, 15 through 20. The probability is 6/20, or 30%.

Does this calculator show the chance of exactly one success?

No. It calculates the chance that at least one die reaches the target. Exact-one probability requires a different calculation that also counts outcomes where the other dice fail.

Why does rolling more dice increase the chance of at least one success?

Each additional independent die creates another opportunity to succeed. The chance of no successes falls to (1 − p) raised to the number of dice, and subtracting that from 1 gives the chance of at least one.

Are d20 results always equally likely?

The formula assumes each face is equally likely. Physical imperfections, rolling method, or nonstandard dice can violate that assumption, so the result may not describe those rolls exactly.

How to Choose

First check that you need a threshold probability on a standard d20, rather than an average, a particular exact result, or a full game-rule calculation. Then decide whether the question is about one roll or multiple independent dice; this calculator’s main output specifically covers at least one success across the entered number of dice. Enter the target exactly as written in the rule, including whether the threshold is “or higher,” and verify any modifiers before interpreting the percentage. If the game uses advantage, rerolls, or other special mechanics, use a calculation designed for those rules instead.

Final Thoughts

A d20 probability is straightforward once you count the successful faces and clarify what multiple rolls mean. This calculator gives a quick, transparent estimate for a target or higher, while its fair-die and independence assumptions mark where a more detailed model is needed.

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in target | Target number or higher | - | 15 | 1
in dice | Number of d20s | - | 1 | 1
out prob | Chance of at least one success | % | 100 * (1 - ((max(0,min(20,target - 1)) / 20) ^ dice)) | 2
out single | Chance on one die | % | 100 * (1 - max(0,min(20,target - 1)) / 20) | 2