Coin Flip Probability
Coin Flip Probability with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent flips, constant head probability. Counts exactly k heads, not at least k. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Flips n: 10
- Heads k: 5
- Probability of heads: 0.5
Exactly five heads in ten fair flips has probability252/1024=0.24609375.
Frequently asked questions
How do I use this calculator?
Enter flips n, heads k, probability of heads. The result updates automatically. Use Reset to restore the example values.
What method does it use?
P(H=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ. Independent flips, constant head probability. Counts exactly k heads, not at least k. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.