Coin Flip Probability Calculator
Calculate the probability of any heads/tails count in a series of flips using the binomial distribution.
Returns exact and cumulative probabilities.
A coin flip is the simplest probability experiment — but the math behind streaks, consecutive outcomes, and “at least one” calculations surprises most people. Understanding these formulas helps with everything from games to statistical reasoning.
Single flip: P(Heads) = 0.5 (50%) — for a fair coin.
Multiple independent flips: P(All Heads in n flips) = 0.5ⁿ
P(At least one Heads in n flips) = 1 − 0.5ⁿ
Exact count using Binomial Distribution: P(exactly k heads in n flips) = C(n,k) × 0.5ⁿ
Where C(n,k) = n! ÷ (k! × (n−k)!) — the number of ways to choose k items from n.
Worked examples:
Q: What’s the chance of getting exactly 3 heads in 5 flips? C(5,3) = 10 P = 10 × 0.5⁵ = 10 × 0.03125 = 0.3125 (31.25%)
Q: What’s the chance of flipping 5 heads in a row? P = 0.5⁵ = 0.03125 (3.125%) — about 1 in 32
Q: If you flip 10 times, what’s the chance of getting at least one heads? P = 1 − 0.5¹⁰ = 1 − 0.000977 = 99.9%
The Gambler’s Fallacy — important: Each flip is independent. If you’ve flipped 9 heads in a row, the 10th flip is still exactly 50/50. The coin has no memory. Past results do not influence future flips.
Expected number of heads in n flips: Expected Heads = n × 0.5 In 100 flips, you expect 50 heads — but any individual sequence of 100 flips can vary significantly from this expectation.