Coin Flip Odds Calculator
Exact heads odds for any flip count and target.
What it does
Coin flip odds count exact sequences instead of simulating tosses. Ten flips make 1024 ordered outcomes, and the binomial coefficient counts how many carry each head total, giving probabilities that never wobble.
The tool above takes the flip count with a target head count. It returns the exact target chance with the at least chance and the average heads beside them.
The default of 10 flips against 7 or more counts 176 winning sequences of 1024: 17.19%, while exactly 7 lands 120 of 1024 (11.72%). The average sits dead center at 5.
The counting follows Khan Academy probability units with the same binomial tables in LibreTexts statistics references. Both treat fair coins as uniform and independent on every toss.
How to use
- Enter how many times the coin flips, 1 to 100.
- Enter the head count you need, at most the flips.
- Read exactly target first for the precise hit.
- Read target or more for the cumulative chance.
- Use the average to sanity check the middle.
Formula
- C(n,k)
- Sequences with exactly k heads in n flips.
- 2^flips
- All ordered outcomes counted exactly.
- sums
- Cumulative wins from target to all heads.
Targets past the flip count are rejected instead of reading zero. Zero heads wanted always reads 100% for at least, since every outcome qualifies.
Worked example
Example: 10 flips, 7+ heads
Flips 10, target 7.
- Outcomes: 2^10 = 1024.
- Exactly 7: C(10,7) = 120, so 120/1024 = 11.72%.
- Winners: 120 + 45 + 10 + 1 = 176 for 7 through 10.
- At least: 176/1024 = 17.19%. Average 5.
- Tool shows 11.72%, 17.19%, 5 heads.
Reference table
| Target+ | Winners | Chance |
|---|---|---|
| 5+ | 638 of 1024 | 62.30% |
| 7+ | 176 of 1024 | 17.19% |
| 9+ | 11 of 1024 | 1.07% |
| 10 | 1 of 1024 | 0.10% |
Limits
- Fair coins only; weighted coins break uniformity.
- Exact counting capped at 100 flips.
- Independent tosses assumed every flip.
- Streaks carry no memory into the next toss.
Common mistakes
- Reading 50% per flip as 50% for the bundle.
- Expecting balance after a streak (gambler fallacy).
- Counting order blindly on cumulative targets.
- Trusting short runs over exact odds.
- Entering targets past the flip count.
Try it yourself
Quick checks. Answers sit tucked under each question.
2 flips, both heads?
1 of 4: exactly and at least both 25%.
1 flip a head?
1 of 2: 50% exact and at least.
10 flips, 5+ heads?
638 of 1024 = 62.30%.
Questions
Odds of 7 heads in 10 flips?
Exactly 7: 11.72%. Seven or more: 17.19%.
Do streaks matter?
No. Coins hold no memory, so five heads still leaves 50% next.
Why 1024 outcomes?
Each flip doubles sequences: 2^10 = 1024 ordered results.
Exact vs at least?
Exact counts one total; at least sums that total upward through all heads.
What is C(10,7)?
120 sequences: 10! / (7! x 3!).
Fair coin required?
Yes. Biased coins need their own weighted math.