Coin Flip Probability Calculator
Odds of getting a number of heads in N flips.
Enter your values
Enter the number of flips you are working with.
Enter the heads wanted you are working with.
Enter the chance of heads in %.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Odds of getting a number of heads in N flips. |
|---|---|
| Category | Math |
| Inputs needed | Number of flips, Heads wanted, Chance of heads |
| Main output | Exactly 7 heads |
| Formula | P(k) = C(n,k) × p^k × (1−p)^(n−k) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Number of flips
- Enter the number of flips you are working with.
- Heads wanted
- Enter the heads wanted you are working with.
- Chance of heads(%)
- Enter the chance of heads in %.
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.
What do I need to enter into the Coin Flip Probability Calculator?
Just 3 values: number of flips, heads wanted, chance of heads. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Coin Flip Probability Calculator work out the answer?
The chance of exactly k heads in n fair flips is C(n,k) ÷ 2ⁿ. It applies the formula P(k) = C(n,k) × p^k × (1−p)^(n−k) and shows the working so you can check each step by hand.
Is the Coin Flip Probability Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.