OddsCalc

Coin Toss Probability Calculator

What are the odds of that many heads?

Number of Flips

Heads Wanted

Exactly This Many

24.61%

At Least This Many: 62.3%
Combinations: 252

What you entered

Number of Flips: 10Heads Wanted: 5

1
Ways to get exactly this many heads
C(10, 5)= 252
2
Total possible outcomes
2^10= 1,024
3
Probability of exactly this many heads
252 / 1,024= 24.6094%
4
Probability of at least 5 heads
sum of C(10, k) / 2^10 for k = 5..10= 62.3047%

Result

Exactly This Many: 24.61%

Probability of getting a given number of heads

Exact probability is the number of ways to arrange that many heads, divided by 2 to the power of the flips. 'At least' sums every outcome from that count upward.

Flips	Heads	Ways	Exactly	At least
1	1	1	50.00%	50.00%
2	1	2	50.00%	75.00%
2	2	1	25.00%	25.00%
4	2	6	37.50%	68.75%
5	3	10	31.25%	50.00%
10	5	252	24.61%	62.30%
10	7	120	11.72%	17.19%
10	10	1	0.10%	0.10%
20	10	184756	17.62%	58.81%

Exactly half heads becomes less likely as you flip more, not more likely: 50% on two flips, 24.61% on ten, 17.62% on twenty. What converges toward one half is the proportion, not the exact count.

Why five heads in ten flips is not 50%

Exactly five heads in ten flips happens only about 24.6% of the time. Half is the average outcome, not the likely one — there are many ways to land near the middle and each individual result, including the exact midpoint, takes only a slice of the probability.

The coin has no memory

After six heads in a row, the seventh flip is still 50/50. Sequences of runs look surprising because we underestimate how common streaks are in random data, but each toss is independent — the gambler's fallacy is expecting the coin to correct itself.

Frequently asked questions

What are the odds of flipping 10 heads in a row?

Exactly (1/2)^10 = 1 in 1,024, or about 0.098%. It sounds rare, but if you flip 10 coins 1,000 times, you'd expect it to happen roughly once.

How is coin toss probability different from dice roll probability?

Coin tosses are binary (2 outcomes per flip), making the math straightforward binomial probability. Dice rolls have 6+ outcomes per die, and summing multiple dice creates a bell-curved distribution rather than a symmetric binomial one.

I need to flip at least 7 heads out of 10 — what's the probability?

P(7 or more heads in 10 flips) = C(10,7)/1024 + C(10,8)/1024 + C(10,9)/1024 + C(10,10)/1024 = (120 + 45 + 10 + 1)/1024 = 17.2%. More likely than you'd expect.

Are real coins actually fair?

Nearly, but not perfectly. Research shows a slight bias (~51%) toward the side facing up when flipped, due to the physics of the toss. For practical purposes, this bias is negligible — it would take thousands of flips to detect statistically.