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Coin Flip Probability Calculator
This is a probability calculator rather than a virtual coin: it works out how likely a result is over a series of flips. Enter the number of flips and a number of heads to get the chance of exactly, at least or at most that many, for a fair coin or a weighted one, with a table of every outcome.
- Odds
- 1 in 4.1
- Expected number of heads
- 5
- Standard deviation
- 1.58
- Chance every flip lands the same
- 0.2%
Chance of every number of heads
| Heads | Exactly | At least | At most |
|---|
Saved setups
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Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Enter the number of flips, up to 500.
- Choose exactly, at least or at most.
- Enter the number of heads you are asking about.
- Leave the chance of heads at 50% for a fair coin, or change it for a biased one.
Worked examples
Exactly 5 heads in 10 flips of a fair coin (252 of 1,024 sequences)
- Probability
- 24.61%
- Odds
- 1 in 4.1
- Expected number of heads
- 5
- Standard deviation
- 1.58
At least 8 heads in 10 flips (45 + 10 + 1 = 56 of 1,024 sequences)
- Probability
- 5.47%
- Odds
- 1 in 18.3
Three heads in a row
- Probability
- 12.5%
- Odds
- 1 in 8
- Chance every flip lands the same
- 25%
At least 4 heads in 5 flips of a coin weighted 60% toward heads
- Probability
- 33.7%
- Expected number of heads
- 3
- Standard deviation
- 1.1
Why exactly half is not that likely
People expect ten flips to give five heads, but that happens only 24.6% of the time — 252 of the 1,024 possible sequences. Getting 4, 5 or 6 heads covers 65.6% of cases. The more flips, the smaller the chance of an exact 50/50 split: in 100 flips, exactly 50 heads comes up just 8% of the time.
What does tighten with more flips is the proportion. In 100 flips, about 95% of the time you will see between 40 and 60 heads.
Streaks and the gambler’s fallacy
The chance that every flip lands heads halves with each flip: 3 in a row is 12.5% (1 in 8), 5 in a row is 3.1% (1 in 32) and 10 in a row is 0.098% (1 in 1,024).
But a coin has no memory. After nine heads in a row, the tenth flip is still 50/50. Believing tails is “due” is the gambler’s fallacy; the long odds apply to the whole streak before it starts, not to the next flip.
The binomial distribution
Coin flips are the classic example of a binomial experiment: a fixed number of independent trials, each with the same two outcomes and the same probability. That means this calculator also answers questions that have nothing to do with coins — set the chance of “heads” to any success rate, such as the chance that at least 4 of 5 free throws go in for a 60% shooter (33.7%).
Questions people ask
What is the probability of getting 5 heads in 10 flips?
24.61% — 252 of the 1,024 equally likely sequences.
What are the odds of 10 heads in a row?
1 in 1,024, or about 0.098%.
What is the probability of at least 8 heads in 10 flips?
5.47%. There are 45 ways to get eight, 10 ways to get nine and 1 way to get ten: 56 out of 1,024.
If I get heads five times in a row, is tails more likely next?
No. Each flip of a fair coin is 50/50 regardless of what came before.