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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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