Statistics Calculators

Coin Flip Probability Calculator

Calculate the probability of getting exactly, at least, or at most a certain number of heads in a series of coin flips.

P(exactly k heads) —

P(at least k heads) —

P(at most k heads) —

About the Coin Flip Probability Calculator

Coin flips follow the binomial probability model: each flip is an independent trial with two outcomes. This calculator finds the probability of landing exactly k heads, as well as the cumulative probability of at least or at most k heads, across n flips.

Formula: P(X = k) = C(n, k) × pᵌ × (1 − p)ᵉ⁻ᵌ, where p is the probability of heads on a single flip

For a fair coin (p = 50%), getting exactly half heads becomes less likely as n grows even though it remains the single most probable outcome, since the total probability spreads across more possible values.