Coin Toss Probability Calculator
Calculate the odds of getting heads or tails over multiple coin tosses.
Chance of exactly 5 heads
24.6%
Out of 10 tosses of a fair coin.
Probability
0.246094
Expressed as a decimal between 0 and 1.
Expected heads
5
Expected tails
5
- Runs entirely in your browser
- No data is stored
- Free forever
What is this calculator?
This calculator works out how likely a given run of heads is. Enter how many times you plan to flip a fair coin and how many heads you want, and it returns the exact probability, the same number as a percentage, and the heads and tails you should expect on average. It is a friendly way to see why ten heads in a row is rare but not impossible.
How does it work?
We use the binomial formula: the number of ways to choose your heads from the total tosses, multiplied by one half raised to the power of the number of tosses. Expected heads and tails are simply half the tosses each, because a fair coin has no memory.
Frequently asked questions
Does a coin remember previous flips?+
No. Every toss is independent, so a run of heads does not make tails any more likely on the next throw.
Why is exactly half heads not certain?+
Half is the single most likely outcome, but there are many other results, so its individual probability is well below 100%.
What formula is used here?+
The binomial probability formula: the number of ways to pick your heads from the tosses, times one half raised to the number of tosses.
How rare is ten heads in a row?+
About 0.098%, or roughly one run in every 1,024 attempts of ten tosses.
Does this assume a fair coin?+
Yes. Both faces are treated as equally likely, which is close enough for any ordinary coin.
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