Flip a Coin

Three steps and no setup. First, throw the coin: tap it, press the FLIP button, or hit the Space bar from anywhere on the page. Second, decide how many you want in the air — the stepper takes anything from 1 to 100, and the presets jump straight to 1, 2, 5, 10, 50 or 100 for the common cases. Third, read the panel underneath, which updates on every throw with the running split, the longest runs, the streak in progress and the convergence chart. Two optional modes change what the coin is for rather than how it works: calling a side before the flip turns it into a game with a win rate, and custom labels replace heads and tails with your own two options so the answer reads back as the actual decision.

Every outcome on this page comes from crypto.getRandomValues, the Web Crypto API generator that browsers seed from the operating system entropy pool and use to produce cryptographic keys. Each flip draws a 32-bit value and compares it against a threshold scaled from your chosen heads probability across the full range. At the default 50% that threshold falls at exactly half the range, so heads and tails are equally likely with no rounding bias and no special-casing — a fair coin is simply the midpoint of the same arithmetic that produces a weighted one. The common alternative, Math.random, is a fast pseudo-random generator whose internal state can be reconstructed from enough observed output; for deciding who buys coffee the difference is academic, but if the point is to demonstrate genuine randomness it is worth using the generator that actually provides it. The result is also drawn before the coin starts spinning. The animation is told which face to land on, so nothing about the timing of your click, the speed of the tumble or how long you hold the button can influence the outcome.

Very nearly, and the way it falls short is not the way most people guess. Persi Diaconis, Susan Holmes and Richard Montgomery modelled human coin flipping in 2007 and predicted that a coin tends to land on the side it started on, because a thumb flip imparts a slight off-axis wobble instead of a clean rotation about a single axis. In 2023 Frantisek Bartos and colleagues put the prediction to the test with 350,757 recorded flips and found the same-side probability was 0.508, with a 95% credible interval from 0.506 to 0.509 — small, far too consistent to be noise, and varying noticeably between individual flippers. The bias is towards the starting side, not towards heads, which is why calling the toss while the coin is already in the air removes most of it. Spinning a coin on a table is a different and much worse proposition, because the milled edge is not perfectly symmetrical and the coin tends to topple towards its heavier face. A simulated flip has no starting side, no wobble and no flipper, which is precisely why it is the fairer of the two.

Each flip is independent, so the chance of a specific run of length n is one half multiplied by itself n times. The numbers below are for calling the run in advance — the odds that a streak of some length appears somewhere in a long session are far higher, which is why a run of ten in a thousand flips is ordinary rather than remarkable. As a rule of thumb the longest streak in n flips is around log2(n).

The coin is not really a randomiser in most of these situations — it is a commitment device. Two people who cannot agree use it because neither has to concede, and the outcome carries no argument with it. Sport uses it for the same reason: the NFL, cricket and tennis all start with a toss precisely because it gives neither side a grievance about who chose first. Classrooms use it because it is the cheapest way to make probability tangible, and the export on this page exists so a class can run a thousand trials in a minute and take the data into a spreadsheet rather than tallying by hand. Elections have used it too — several US states break tied local races by lot, and a 2013 Philippine mayoral race was decided on a coin toss. And there is the private use nobody admits to: flipping to decide, then noticing which result you were quietly hoping for. That is worth more than the coin, and it is the one outcome the statistics on this page cannot measure.

The Romans called it navia aut caput — ship or head — after the coins of the period, which carried the head of Janus on one face and the prow of a ship on the other. The game was not purely chance to them: the outcome was sometimes read as an expression of divine will rather than a random event, which made it a legitimate way to settle a dispute. In medieval England the same game was cross and pile, named for the cross stamped on one side and the pile, the lower die used to strike the coin, on the other. The modern names are more prosaic: heads for the monarch or president in profile, tails for whatever is on the reverse. The practice of tossing rather than spinning is comparatively recent, and it is the better method — as the 2023 flip study showed, tossing carries a bias under 1%, while spinning a coin on a table can skew several percent towards the heavier face.

Tap the coin, press the FLIP button, or hit the Space bar — the result appears immediately and no signup is involved. Two steppers sit above the coin: how many coins go up together, and how many times to repeat that throw. Everything runs inside your browser, so it works offline once the page has loaded and nothing about your flips is sent anywhere. If you want the coin to answer a real question rather than say heads or tails, turn on custom labels and put your two options on the faces instead.

Yes. Each outcome is a value drawn from crypto.getRandomValues, the Web Crypto API generator that browsers seed from the operating system entropy pool and use for cryptographic key material. It is not Math.random, whose internal state can be reconstructed from enough output. At the default 50% setting the comparison threshold sits at exactly half the 32-bit range, so heads and tails are precisely equally likely with no rounding bias. Flip a few thousand times and the convergence chart will show the split settling on 50%.

As many as you like. One click covers up to 100 coins repeated up to 1,000 times, which is 100,000 outcomes, and the running statistics accumulate across every click on top of that. Set "how many flips" to 100 and the convergence chart draws the whole run rather than a single point, which is what makes the law of large numbers visible. Auto-flip in the settings keeps throwing on a timer if you want to build a sample hands-free. Nothing is rate limited and there is no daily cap.

On this page, neither — the generator gives both sides exactly equal probability. On a real coin the answer is slightly more interesting. Diaconis, Holmes and Montgomery modelled human coin flipping in 2007 and predicted a small bias towards the side the coin started on, because a thumb flip introduces a wobble rather than a clean rotation. Bartos and colleagues tested this in 2023 with 350,757 recorded flips and measured the same-side probability at 0.508. Note that is a bias towards the starting side, not towards heads.

It is a way for three people to settle something with one round instead of a bracket. All three flip at the same time and whoever lands the odd result out — the only heads among two tails, or the only tails among two heads — is the winner or the loser, depending on what you agreed first. It fails when all three match, which happens on a quarter of rounds, so you simply flip again. Set the coin count to 3 here and the running tally does the counting for you.

On a real coin, yes, though rarely. A 1993 analysis by Murray and Teare estimated the odds for an American nickel landing on edge on a hard surface at roughly 1 in 6,000, and the thicker the coin relative to its diameter the more often it happens. A digital flip has no third state: the generator produces one of exactly two outcomes, so an edge landing is not something this tool models. If you need a genuine third option, flip twice and treat the four combinations as your outcomes.

Close to it, but not perfectly. The 2023 study by Bartos and colleagues collected 350,757 flips and found coins landed on the side they started on 50.8% of the time, with a 95% credible interval of 0.506 to 0.509 — small, consistent, and varying noticeably between individual flippers. Spinning a coin on a table is far worse than flipping it, because the milled edge is not symmetrical and the coin tends to fall towards the heavier face. Calling the toss while the coin is in the air removes most of the flipping bias.

A weighted or biased coin is one where the two outcomes are not equally likely. Use the heads probability slider to set anything from 0 to 100%; tails is always the remainder, so the two can never be configured to something that does not sum to 100. It is useful for demonstrating what unfair odds actually look like over many trials, and for testing code that consumes a biased stream. Whenever the value is not 50 the page shows a warning badge, and the session is excluded from the all-time run records so a rigged run cannot pollute statistics that claim to describe a fair coin.

The gambler's fallacy is the belief that a run of one outcome makes the other outcome overdue. It does not: the coin has no memory, so after eight heads the ninth flip is still exactly 50/50. What confuses people is that long runs feel impossible while being completely ordinary — in n flips the longest streak is roughly log2(n), so about 7 in 100 flips and about 10 in 1,000. Watch the current run counter climb on this page while the heads percentage stays near 50 and the fallacy stops being persuasive.

It says that as a sample grows, its average converges on the true underlying probability. The chart on this page draws it live: at twenty flips the heads percentage swings wildly and often sits at 30% or 70%, but by a few thousand it hugs the 50% line. The subtlety worth knowing is that what converges is the ratio, not the gap. The raw difference between heads and tails counts typically grows with the square root of the number of flips, so a run can end 5,060 to 4,940 — a gap that widened in absolute terms while the percentage tightened.

Two. Waiting for the first success in repeated independent trials follows a geometric distribution, and its expected value is one divided by the probability of success — so at a 50% chance the average wait is 1 / 0.5, which is 2 flips. That is an average, not a guarantee: a quarter of attempts take three flips or more, and about one in a thousand takes ten or more. Set the heads probability slider to 25% and the expected wait becomes 4 flips, which you can watch play out in the run counter.

Google's widget flips one coin, once, and shows you the answer — which is all most people need. This page is built for the part it does not cover: throwing up to 100 coins at a time, calling the side before it lands and keeping a win rate, putting your own labels on the faces, setting unfair odds deliberately, and tracking streaks, alternations and a convergence chart across the whole session. It also states its randomness source openly and persists your statistics on your device between visits.