Flipping a coin is the classic way to settle a decision. This one uses your device’s secure random number generator, so each flip is fair and independent.
Flip a single coin, or up to a thousand at once if you want to see how lumpy random really looks.
How to use the Coin Flipper#
- Choose how many flips. Leave it at 1 for a single toss, or enter more.
- Press Flip. The coin lands on heads or tails at random.
- Flip again. Press the button for a fresh result.
How the flip works#
Each flip is a random bit from your browser’s cryptographic random source. Heads and tails each have a 50 percent chance, and the previous result has no effect on the next one.
What to expect from 100 and 1,000 flips#
Even with a perfect coin, the count of heads wobbles around half. In 100 flips, about 95 percent of results fall between 40 and 60 heads, because the standard deviation is √(100 × 0.5 × 0.5) = 5 and the usual range is two deviations either side of 50. For 1,000 flips the standard deviation is about 15.8, so 95 percent of runs land between roughly 469 and 531 heads. The percentage gets closer to 50 as you flip more, even though the raw gap between heads and tails often grows.
| Flips | Expected heads | Likely range (95%) | Typical longest streak |
|---|---|---|---|
| 10 | 5 | 2 to 8 | 3 to 4 |
| 100 | 50 | 40 to 60 | 6 to 7 |
| 1,000 | 500 | 469 to 531 | 9 to 10 |
Streaks are normal#
People expect a fair coin to alternate and are surprised by long runs. In 100 flips, a run of six heads or tails in a row is more likely than not, and the longest streak in n flips is typically close to log₂(n). Each flip is independent: the coin has no memory, so after five heads the chance of heads on the next flip is still one half. Believing that tails is “due” is called the gambler’s fallacy. The calculator shows the longest streak in your set so you can see how common they are.
Is a flip really 50-50, and is this one fair?#
A real coin is very close to fair but not perfectly so. A study by the statistician Persi Diaconis and colleagues found that a coin tends to land on the same face it started on about 51 percent of the time, because of how it wobbles in the air. This flipper uses the random number generator built into your browser, which is designed for security, so heads and tails are equally likely. Use it to settle a small choice, to teach probability or to simulate a series of trials for a school project. For chances of events happening, see the risk calculator.
Frequently asked questions#
For this tool, yes. Real coins can have tiny biases, but they’re small.
In n flips, about log base 2 of n. For 1,000 flips, around ten.
It is as close as a computer can get for everyday purposes. This flipper takes random numbers from the browser’s cryptographic generator, which draws on unpredictable system sources, and uses the lowest bit of each to choose heads or tails. The result is not influenced by earlier flips.
Because small samples vary a lot. With 10 flips, 7 heads and 3 tails happens about 12 percent of the time even with a fair coin. The gap does not mean the coin is biased. Flip many more times and the percentages will move closer to 50 percent.
It is fine for small choices, such as who goes first. For big decisions, it can help in another way: notice how you feel when the coin lands. If you are disappointed with the result, that tells you what you wanted. For anything important, though, weigh the facts first.