Coin Flip Probability Calculator
Uses the binomial distribution to find the probability of getting exactly x heads in n coin flips, plus the cumulative probability of x or fewer heads, for any heads probability.
What this calculator does
The Coin Flip Probability Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Uses the binomial distribution to find the probability of getting exactly x heads in n coin flips, plus the cumulative probability of x or fewer heads, for any heads probability. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Coin Flip Probability Calculator
This coin flip probability calculator applies the binomial distribution. For exactly x heads in n flips it computes nCx × p^x × (1 − p)^(n − x), and it sums those terms from 0 up to x for the cumulative probability of x or fewer heads.
Set the probability of heads to 0.5 for a fair coin, or any value between 0 and 1 for a biased coin.
Formula & Mathematical Calculation
P(exactly x heads) = f(Number of flips (n), Number of heads (x), Probability of heads)
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
For n = 10 flips, x = 5 heads, and p = 0.5: P(exactly 5) = nCr(10,5) × 0.5^5 × 0.5^5 = 252 ÷ 1024 ≈ 24.6094%. The probability of 5 or fewer heads is 638 ÷ 1024 ≈ 62.3047%.
Key Benefits
- Gives both the exact-count probability and the cumulative probability at once
- Works for fair or biased coins by setting any heads probability from 0 to 1
- Reports results as percentages rounded to four decimals
How to Use this Calculator
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Enter the number of flips (n)
Type how many times the coin is flipped into the Number of flips field, for example 10. -
Enter the number of heads (x)
Type the target number of heads into the Number of heads field; it must be between 0 and n. -
Enter the probability of heads
Type the chance of heads on a single flip, such as 0.5 for a fair coin, then select Calculate.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Coin Flip Probability Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.