Coin Flip Probability Calculator
Odds of getting a number of heads in N flips.
Enter your values
ⓘ Live results
Results
- Exactly 7 heads
- 11.7188%
- At least 7 heads
- 17.1875%
- At most 7 heads
- 94.5313%
- Expected heads
- 5
- Odds of exactly k
- 1 in 8.5
Working
- 1P = C(10,7) × 0.5^7 × 0.5^3 = 0.117188
Quick answer
The chance of exactly k heads in n fair flips is C(n,k) ÷ 2ⁿ.
P(k) = C(n,k) × p^k × (1−p)^(n−k)
How to use the Coin Flip Probability Calculator
- 1Enter how many times the coin is flipped.
- 2Enter how many heads you're asking about.
- 3Adjust the bias if the coin isn't fair.
Worked example
Using the values the calculator loads with:
Inputs
- Number of flips10
- Heads wanted7
- Chance of heads50 %
Results
- Exactly 7 heads11.7188%
- At least 7 heads17.1875%
- At most 7 heads94.5313%
- Expected heads5
- Odds of exactly k1 in 8.5
- P = C(10,7) × 0.5^7 × 0.5^3 = 0.117188
Frequently asked questions
Are 10 heads in a row possible?
Yes — about 1 in 1,024. Rare but far from impossible over many attempts.
Does a run of tails make heads more likely?
No. Each flip is independent; believing otherwise is the gambler's fallacy.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.