DnD Dice Calculator: 5e Advantage and Dice Pool Odds

Calculate exact hit probabilities against target DC / Armor Class, Advantage vs Disadvantage math, and multi-dice damage averages.

D20 success odds and average damage: how they are calculated

On a d20, the chance of success is (21 − minimum roll needed) / 20, where the minimum roll is the DC minus your modifier. With advantage it becomes 1 − (1 − p)², with disadvantage p²: against DC 15 with +5, 55% turns into 79.75% or 30.25%.

D20 mode

Minimum die result: DC (or AC) − modifier, clamped between 1 and 20. Single-die probability: p = (21 − minimum) / 20. The tool treats a natural 20 as a success and a natural 1 as a failure on every roll, so p never drops below 5% or exceeds 95%. The D&D 5e core rules apply this only to attack rolls; for an ability check the real result can be 0% or 100%.

  • Normal: p; critical hit 5%.
  • Advantage (2d20, keep highest): 1 − (1 − p)²; critical 9.75%.
  • Disadvantage (2d20, keep lowest): p²; critical failure 9.75%.
  • Elven Accuracy (3d20, keep highest): 1 − (1 − p)³; critical 14.26%.

Example

DC 15 with a +5 modifier: you need 10 or more, 11 faces out of 20, so 55%. With advantage: 1 − 0.45² = 79.75%. With disadvantage: 0.55² = 30.25%. With Elven Accuracy: 90.89%. Against DC 25 with +3, only a natural 20 works: 5%.

Damage pool mode

Average of an s-sided die: (s + 1) / 2. For 4d6 + 3: 4 × 3.5 + 3 = 17.0 on average, from 7 to 27. For 2d8 + 4: 13.0. The threshold in this mode is only used by the simulated roll; the tool does not compute the probability of reaching it with several dice.

Frequently Asked Questions

How much does advantage add to my d20 odds?

It depends on the base chance. At 55%, advantage raises success to 79.75%, almost 25 points more; the gain peaks around 50% and shrinks at the extremes.

What is the chance of a natural 20 with advantage?

It is 1 − (19/20)², or 9.75%, compared with 5% on one die. With three dice (Elven Accuracy) it rises to 14.26%.

What is the average of 4d6?

Each d6 averages 3.5, so 4d6 average 14; with a +3 bonus, 17.0. Results range from 7 to 27.

What are my odds against DC 15 with +5?

You need 10 or more on the die, 11 faces out of 20: 55% on a normal roll and 30.25% with disadvantage.

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

Is my data protected?

Yes. All processing is performed directly and securely inside your browser. No personal data is sent to our servers.