A fair coin has a 50% chance of heads on each flip — this finds the probability of getting exactly (or at least) a certain number of heads across many flips.
How it works
Using the binomial probability formula with the success probability fixed at 50%, the number of ways to choose which flips land heads is combined with the fixed per-flip probability.
What this does not include
This does not include unfair (biased) coins or general trial probabilities — for those, use this site’s full binomial probability calculator instead, which accepts any success probability.
How to use this calculator
- Enter the number of flips and how many heads you want the probability for.
A worked example
10 coin flips, probability of exactly 5 heads: 24.609375%.
2 flips, probability of exactly 1 head: 50%.
What the variables mean
| Variable | Meaning |
|---|---|
| Flips | Total number of coin flips |
| Heads | The exact number of heads being asked about |
Edge cases worth knowing
More flips doesn’t make an exact outcome more likely. Getting exactly 5 heads in 10 flips has only about a 24.6% chance, even though 5 is the “expected” number — more possible outcomes spread the probability thinner as flip count grows.
Requesting more heads than there are flips is impossible, so the calculator declines to show a result for that combination.
Frequently asked questions
Why isn’t 5 heads out of 10 flips a 50% probability?
Because there are many possible outcomes for 10 flips, and while 5 heads is the single most likely exact count, it’s still just one of many possible results — its probability is about 24.6%, not 50%.
What’s the difference between “exactly” and “at least”?
“Exactly” gives the probability of that one specific count; “at least” sums the probabilities of that count and every higher count, answering a broader question.
Does the coin need to be perfectly fair for this to apply?
Yes — this calculator assumes exactly 50/50 odds on each flip; a biased coin would need the general binomial probability calculator instead.
