Coin Flip Probability Calculator
How likely is it to get k heads in n flips?
Your numbers
Your results
Exactly k heads
Exactly k heads
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At least k heads
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At most k heads
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Expected heads
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Coin Flip Probability Calculator by TheCalcTools
How the Coin Flip Probability Calculator works
Enter how many times you flip and how many heads you are interested in.
Each flip is independent with the same probability.
The result comes from the binomial distribution.
The formula
P(k heads) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ
Worked example
Using the default values shown in the calculator:
| Number of flips | 10 |
|---|---|
| Number of heads | 7 |
| Chance of heads (%) | 50 |
- P(exactly 7 heads in 10 flips) = 120 ÷ 1024 = 11.72%.
- P(at least 7 heads) = 17.19%.
- The expected number of heads is 5.
Result:
| Exactly k heads | 11.72% |
|---|---|
| At least k heads | 17.19% |
| At most k heads | 94.53% |
| Expected heads | 5.00 |
Frequently asked questions
Does a streak of heads make tails more likely?
No. Each flip is independent, so past flips do not change the next one. That belief is called the gambler’s fallacy.
What is the most likely number of heads?
For a fair coin it is n ÷ 2, although any single exact count becomes less likely as n grows.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.