Coin Flip Probability Calculator
Calculate coin flip probability using your data.
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What this tool does
Calculate coin flip probability using your data. Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
How to use the Coin Flip Probability Calculator
- Enter or select number of flips (n).
- Enter or select heads (k).
- Enter or select probability of heads per flip (%).
- Read the calculated result; change any measurement to compare alternatives.
Formula
binomial model: P(X=k) = C(n,k) p^k (1−p)^(n−k)
- nn
- Number of flips (n)
- kk
- Heads (k)
- pp
- Probability of heads per flip (%)
Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
Worked example
For coin flip probability calculator, the following measurements illustrate the exact method: Number of flips (n): 10; Heads (k): 5; Probability of heads per flip (%): 50.
Inputs
- Number of flips (n)10
- Heads (k)5
- Probability of heads per flip (%)50
Result
- P(exactly k heads) (%)24.61
- P(at most k heads) (%)62.3
- P(at least k heads) (%)62.3
- Expected heads5
Results explained
- P(exactly k heads) (%)
- P(exactly k heads) (%) from the formula above. Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
- P(at most k heads) (%)
- P(at most k heads) (%) from the formula above. Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
- P(at least k heads) (%)
- P(at least k heads) (%) from the formula above. Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
- Expected heads
- Expected heads from the formula above. Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
Frequently asked questions
binomial model: P(X=k) = C(n,k) p^k (1−p)^(n−k)
Flips are independent; a fair coin uses p = 50%. A streak does not change the next flip's probability (the gambler's fallacy).
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.