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Coin flip probability: the chance of heads, flip by flip

The chance of heads in any number of flips, exactly, at least or at most, with streaks and the range 95 runs in 100 fall in.

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Every try has the same chance and does not depend on the ones before it. Type the chance your own game or situation has: the starting figures are examples. A 1-in-6 chance is 16.67%.

24.6%chance it happens exactly 5 times in 10 tries
99.9%chance it happens at least once in 10 tries
5times it happens on average in 10 tries
2 to 8times it happens in 10 tries, in 95 runs out of 100
10.9%chance of 5 in a row somewhere in 10 tries
4tries before at least one is 90% likely

In 10 tries with a 50% chance each, the chance that it happens exactly 5 times is 24.6%. On average it happens 5 times, and in 95 runs out of 100 it happens between 2 and 8 times. A streak of 5 in a row turns up somewhere in those tries 10.9% of the time.

Chance of each count in 10 tries at 50% each
Times it happensExactly this manyThis many or moreThis many or fewer
00.0977%100%0.0977%
10.977%99.9%1.07%
24.39%98.9%5.47%
311.7%94.5%17.2%
420.5%82.8%37.7%
524.6%62.3%62.3%
620.5%37.7%82.8%
711.7%17.2%94.5%
84.39%5.47%98.9%
90.977%1.07%99.9%
100.0977%0.0977%100%

Check it with pretend runs

Pretend runs make every try with a random number from your browser and the chance above, then count what happened. There is no money in it, and it is not any app’s game. The exact figures above never change; the pretend ones wobble from press to press, and that wobble is what chance looks like.

Flip a coin 10 times and you expect 5 heads, yet 95 runs out of 100 give anything from 2 to 8 heads. The exact middle count happens 24.6% of the time, which surprises many people. The calculator lets you change the number of flips and the question.

Try 100 flips with the buttons above. Exactly 50 heads falls to about 8%, and a streak of 7 heads in a row turns up in nearly a third of runs. More flips make the average steadier and the exact count rarer.

The calculator runs in your browser and sends nothing anywhere, so you can try any figures you like.

Common questions

Does a coin remember its last flips?

No. Each flip is a fresh 50-50 chance whatever came before. After five heads in a row the next flip is still 50% heads. The chance of five heads in a row was small before you started, but once it has happened it does not change the next flip.

Why is exactly half heads so unlikely?

Because many nearby counts are almost as likely and they share the chance. In 10 flips exactly 5 heads is 24.6%, and in 100 flips exactly 50 heads is 7.96%. The middle count is still the likeliest single count, but it is never likely in the way people expect.

How long a streak of heads should I expect?

In 100 fair flips a run of 7 or more heads turns up about 32% of the time, and a run of 5 or more about 81% of the time. Streaks are an ordinary feature of random flips, not evidence of a rigged coin or a pattern.

What does it mean that tries are independent?

It means one try does not change the chance of the next. Coin flips and dice rolls are like that. Drawing cards from a deck without putting them back is not, because each card drawn changes what is left. The calculator assumes independent tries with the same chance.

Can a probability calculator say what the next try will be?

No. It says how often something happens over many tries. For one try the answer is only the chance, and the chance does not move because of what happened before. Nothing here predicts a single result.

More on the probability calculator

Binomial distribution probability calculatorBinomial distribution probability calculator. Binomial probability for 20 tries at 30% each: exactly 6 is 19.2%, with the full table of counts below.

The full tool

Probability calculatorThe full probability calculator, with every setting.