Coin Flip Probability Calculator

About this calculator

Flipping a fair coin n times is the textbook example of a binomial distribution: each flip is an independent trial with a 50% chance of heads, and the probability of getting exactly k heads is given by P(k) = C(n,k) × 0.5ⁿ, where C(n,k) counts the number of ways to choose which k flips land heads.

This calculator computes that exact probability along with the cumulative probability of getting at least k heads, and the expected number of heads over n flips (always n/2 for a fair coin). It’s a go-to example in introductory probability and statistics courses, and the same math underlies fairness checks in game design and simple demonstrations of random processes in decision theory.