D&D Dice Probability

Understanding dice rolls and modifiers helps you plan turns and interpret results. This guide explains how the Dice Probability tool works: die type, modifier, and “meet or exceed” target. The math is exact for fair dice; use it for planning and fun, not real-world prediction.

What it's for

Use the calculator when you want to know the probability of rolling a certain number or higher on a die (d4, d6, d8, d10, d12, d20), with an optional modifier. You can ask “What’s the chance I roll at least 15 on a d20 with +5?” and get the exact percentage. Useful for D&D, other RPGs, and game design.

Step by step

Choose dice — d4, d6, d8, d10, d12, or d20. Each face is equally likely.
Enter modifier — Optional + or − (e.g. +5 for a strength check). The modifier is added to the roll.
Enter target (optional) — The number you want to “meet or exceed.” The calculator shows the probability (as a percentage) of (roll + modifier) ≥ target.
Read the result — Probability distribution and/or “meet or exceed” percentage. For a d20 with no modifier, the chance to roll ≥ N is (21 − N) × 5%. With a modifier, the effective target shifts.

Formula

Fair die — Each face has probability 1/n (n = number of sides). Average roll = (n + 1) / 2.
Meet or exceed target T with modifier M: you need roll ≥ (T − M). So probability = number of outcomes where roll ≥ (T − M), divided by n. If (T − M) is above the max roll, probability = 0; if (T − M) is 1 or below, probability = 1.

Example: d20, modifier +5, target 15. You need roll ≥ 10. Outcomes 10–20 = 11 outcomes. Probability = 11/20 = 55%.

Example

d20, no modifier, target 15: Need natural roll ≥ 15 → 6 outcomes (15–20) → 30%.
d20, +5, target 15: Need roll ≥ 10 → 11 outcomes → 55%.
d6, modifier 0, target 4: Need roll ≥ 4 → 3 outcomes (4, 5, 6) → 50%.

Tips