About Coin Flip
Press Flip and you get Heads or Tails, each with a 50% chance. Raise How many flips to anything up to 500 and the tool lists every flip in order and adds a tally: the number of heads, the number of tails, the percentage of each and the total. That makes it useful for two different jobs. One flip settles who goes first or which option wins. A batch of 100 or 500 is a ready-made probability experiment, with a list you can copy or download as a text file for a class or a spreadsheet. The result is shown as plain text, without a coin animation, so a 500-flip run appears instantly.
What to expect when you flip a coin 10, 20, 50, 100 or 500 times
Exact binomial probabilities for a fair coin. The share of heads settles towards 50% as the number of flips grows, while hitting exactly half becomes less likely.
| Flips | Chance of exactly half heads | Chance heads are between 40% and 60% | Heads range that covers |
|---|---|---|---|
| 10 | 24.61% | 65.63% | 4 to 6 |
| 20 | 17.62% | 73.68% | 8 to 12 |
| 50 | 11.23% | 88.11% | 20 to 30 |
| 100 | 7.96% | 96.48% | 40 to 60 |
| 500 | 3.57% | More than 99.99% | 200 to 300 |
For 500 flips, 97.75% of runs land between 225 and 275 heads, which is 45% to 55%.
Sample runs from the simulator
Results from real runs of this tool. Every press of Flip is a new random run, so your numbers will differ.
10 flips
How many flips: 10
Tails, Heads, Heads, Tails, Tails, Heads, Heads, Tails, Tails, Tails. Tally: Heads 4 (40%), Tails 6 (60%)
A 4 to 6 split looks uneven but results in the 4 to 6 heads range turn up in about two runs out of three.
50 flips
How many flips: 50
Tally: Heads 22 (44%), Tails 28 (56%), Total flips 50
The longest run in this list was six tails in a row.
100 flips
How many flips: 100
Tally: Heads 45 (45%), Tails 55 (55%), Total flips 100
This run contained a streak of eight identical results, which happens in roughly 3 of every 10 runs of 100.
500 flips
How many flips: 500
Tally: Heads 229 (45.8%), Tails 271 (54.2%), Total flips 500
A lower-than-average heads count for 500 flips, but still inside the 225 to 275 range that covers nearly 98% of runs.
How likely is a streak of heads or tails?
Chance that a list of flips contains at least one run of the same side of the given length, counting runs of either heads or tails.
| Flips | Run of 4+ | Run of 5+ | Run of 6+ | Run of 7+ | Run of 8+ | Average longest run |
|---|---|---|---|---|---|---|
| 10 | 46.5% | 21.7% | 9.4% | 3.9% | 1.6% | 3.7 |
| 20 | 76.8% | 45.8% | 23.7% | 11.5% | 5.4% | 4.7 |
| 50 | 98.1% | 82.1% | 54.4% | 30.9% | 16.2% | 6.0 |
| 100 | More than 99.9% | 97.2% | 80.7% | 54.2% | 31.5% | 7.0 |
| 500 | More than 99.9% | More than 99.9% | More than 99.9% | 98.3% | 86.3% | 9.3 |
People asked to write down a random-looking sequence usually avoid runs longer than three or four, so a list with no long streaks is more likely to be invented than flipped.
Coin flip probability formulas
P(k heads in a row) = (1/2)^k P(exactly k heads in n flips) = C(n, k) / 2^n
Each flip has probability 1/2, and separate flips multiply. For a specific sequence of k results the chance is one half to the power k, so 3 heads in a row is 1/8 and 5 in a row is 1/32. For a count rather than a sequence, C(n, k) is the number of ways to choose which k of the n flips are heads. With 10 flips there are C(10, 5) = 252 ways to get exactly five heads out of 1,024 sequences, which is 24.61%. The expected number of heads is n/2 and the standard deviation is half the square root of n: 5 for 100 flips, about 11.2 for 500.
Ways to use a batch of coin flips
- Classroom probability: have each student flip 100 and record the heads percentage, then compare the spread across the class with the table above.
- Law of large numbers: run 10, then 100, then 500 flips and watch the percentages move towards 50% while the gap in raw counts often grows.
- Streak hunting: download a 500-flip list and find the longest run of one side. It is usually 8 or more.
- Random yes or no for a list: flip once per item and read heads as yes and tails as no.
- Splitting into two groups: flip once per person, heads to one group and tails to the other. The groups will not always be equal in size.
- Best of three or five: set How many flips to 3 or 5 and take the side with the higher count in the tally.
How the simulator decides heads or tails
Every press of Flip starts a new run from a fresh random starting value chosen by your browser. A fast pseudo-random number generator then produces one number between 0 and 1 for each flip: below 0.5 is Heads, otherwise Tails. The flips are independent, so the tool never evens a list out or avoids streaks.
That is suitable for games, decisions and teaching. It is not a certified or cryptographic random source, so do not use it for prize draws, gambling or anything where money or legal fairness depends on the outcome.
There is no weighted or biased coin option, no custom labels in place of Heads and Tails, and no running history between presses: each press replaces the previous result. The largest single batch is 500.
How to use it
- 1
Set How many flips: leave it at 1 for a single toss, or enter any whole number up to 500.
- 2
Press Flip.
- 3
Read Result for a single flip, or the Flips list for a batch.
- 4
Check the Tally for the heads count, tails count and the percentage of each.
- 5
Press Flip again for a fresh set, or copy or download the list first if you need to keep it.