🪙 Coin Flip Probability Calculator
Choose how many times you flip a coin and how many heads you’re interested in to calculate the exact probability, using the binomial distribution.
How Coin Flip Probability Works
Flipping a coin repeatedly is the classic example of a binomial process: each flip is independent and has only two outcomes, heads or tails. This calculator finds the probability of getting a specific number of heads across a series of flips.
The Formula
The probability of exactly k heads in n flips is given by the binomial formula: P(X=k) = C(n,k) × p^k × (1−p)^(n−k), where C(n,k) is the number of ways to choose k heads from n flips and p is the probability of heads on a single flip (50% for a fair coin). “At least” and “at most” sum this formula across the relevant range of outcomes.
- Use the probability field to model a biased coin if needed; leave it at 50% for a fair coin.
Provided for general educational and recreational use.