Coin Flip & Dice Probability Calculator
Calculate the probability of a given number of heads or matching dice rolls.
Assumptions used in this calculation
- Fair coin / fair die: Assumes a fair coin (p=0.5 per flip) or a fair, unweighted die (p=1/6 per face), with each trial independent of the others.
About this calculator
Questions like 'what's the chance of getting exactly 5 heads in 10 coin flips' or 'what's the probability of rolling three sixes in eight dice rolls' feel intuitive but are actually binomial probability problems that require combinatorics most people don't remember from school, computing combinations (C(n,k)) and raising probabilities to a power for every possible outcome. This calculator uses the binomial probability formula, P(exactly k successes in n trials) = C(n,k) × p^k × (1−p)^(n−k), to find the exact probability of a target number of successes across a chosen number of coin flips or dice rolls, along with the cumulative 'at least this many' probability. It's useful for students working through probability homework, or anyone settling a bet or satisfying curiosity about how likely a specific run of flips or rolls actually is. The counter-intuitive part this calculator makes clear is that even the single most likely outcome, like exactly 5 heads in 10 fair flips, still lands well under 50%, since that probability is spread thin across every other possible count.
Worked example
Exactly 5 heads in 10 flips
Result: 24.61%
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