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Coin Flip Probability Calculator
Work out any coin flip probability instantly: the chance of exactly, at least, or at most k heads in n flips, and the odds of a streak of heads somewhere in a run. Answers come as a percent, odds (“1 in …”), and an exact fraction for small runs — with the binomial formula explained below.
Heads in a run of flips
Example: the chance of exactly 5 heads in 10 flips is 252/1024 ≈ 24.6%.
Set the per-flip chance to 0.5 for a fair coin, or change it to model a biased coin. Exact fractions are shown for runs of 30 flips or fewer with a fair coin.
Streak probability
Example: a run of 7+ heads somewhere in 100 fair flips has about a 31.8% chance.
Computes the chance that at least one unbroken run of length s (or longer) appears anywhere in n fair flips. Long streaks are a normal feature of randomness — not proof of a rigged coin.
Quick reference (fair coin)
| Question | Probability |
|---|---|
| Heads on a single flip | 1/2 = 50% |
| Two heads in a row (2 flips) | 1/4 = 25% |
| Exactly 2 heads in 3 flips | 3/8 = 37.5% |
| At least 2 heads in 3 flips | 1/2 = 50% |
| Exactly 5 heads in 10 flips | 252/1024 ≈ 24.6% |
| All heads in 5 flips | 1/32 ≈ 3.1% |
| Ten heads in a row (10 flips) | 1/1024 ≈ 0.098% |
| A run of 2+ heads somewhere in 10 flips | 880/1024 ≈ 85.9% |
| Exactly 50 heads in 100 flips | ≈ 8.0% |
The formula
The probability of getting exactly k heads in n independent flips follows the binomial distribution:
P(X = k) = C(n, k) × pk × (1 − p)n−k
C(n, k) counts how many orderings put the k heads among the n flips, and p is the chance of heads on one flip (0.5 for a fair coin). Worked example — exactly 2 heads in 3 flips: C(3, 2) = 3 orderings (HHT, HTH, THH), each with probability (1/2)³ = 1/8, so P = 3/8 = 37.5%. For “at least” or “at most” questions, add up the matching terms — that is exactly what the calculator above does.
See probability happen
- Interactive statistics simulators — watch the law of large numbers, random walks, the bell curve, and streaks unfold across thousands of simulated flips (great for classrooms).
- Flip a coin 100 times or 1,000 times — run the experiment yourself and compare with the math.
- Live site statistics — the heads/tails split across every flip ever made on this site.
- More reading: coin flip statistics & streak theory · should you choose heads or tails?
Frequently asked questions
- What is the probability of getting heads in a coin flip?
- A fair coin lands heads with probability 1/2 (50%). Each flip is independent, so the chance stays 50% no matter what came before.
- What are the odds of flipping heads twice in a row?
- For a fair coin, two heads in a row has probability 1/2 × 1/2 = 1/4 (25%). Ten heads in a row is 1/1,024 — about 0.098%.
- What formula do I use for coin flip probability?
- Use the binomial formula: the probability of exactly k heads in n flips is C(n, k) × p^k × (1−p)^(n−k), where C(n, k) is the number of ways to choose which flips are heads and p is the chance of heads (0.5 for a fair coin).
- Does the previous flip change the next one?
- No. Coin flips are independent events, so a streak of heads does not make tails "due". Believing otherwise is the gambler's fallacy.
- What is the probability of exactly 50 heads in 100 flips?
- About 8%. Even though 50 is the most likely single count, there are many nearby outcomes (49, 51, 52…), so hitting exactly 50 is fairly rare.