Coin Flip Probability Calculator

Work out coin flip probability instantly with clear inputs, formula shown and shareable results.

About Coin Flip Probability Calculator

Flips follow the binomial distribution: the chance of exactly k heads is C(n, k) p^k (1 - p)^(n - k), and the cumulative tail sums that from k upwards. Seven heads in ten looks unusual but happens about 12% of the time with a fair coin, which is why short streaks are poor evidence of bias.

Formulas

Binomial probability

P(exactly k) = C(n, k) x p^k x (1 - p)^(n - k)

Expected heads

expected = flips x chance of heads

Worked example

With the default values below, Coin Flip Probability Calculator returns Chance of exactly that many heads of 11.7188%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of flipsaccepts 1–200: 10
Heads you are asking aboutminimum 0: 7
Chance of heads on one flipaccepts 0.1–99.9 %: 50 %

Results

Chance of exactly that many heads: 11.7188%
Chance of that many or more: 17.1875%
Heads expected: 5.000
Ways it can happen: 120

Step by step

1Values used
2Binomial probability
3Expected heads
4Chance of exactly that many heads= 11.7188
5Chance of that many or more= 17.1875
6Heads expected= 5.000
7Ways it can happen= 120

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Coin Flip Probability figure worked out?

P(exactly k) = C(n, k) x p^k x (1 - p)^(n - k). Flips follow the binomial distribution: the chance of exactly k heads is C(n, k) p^k (1 - p)^(n - k), and the cumulative tail sums that from k upwards.

Why does this matter?

Seven heads in ten looks unusual but happens about 12% of the time with a fair coin, which is why short streaks are poor evidence of bias.

What do I need to enter?

Enter number of flips, heads you are asking about, chance of heads on one flip. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.