Coin Flip Probability Calculator

For questions about heads and tails, including how surprising a streak really is.

Exactly this many heads

—

Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.

This many or more —

This many or fewer —

At least one streak this long —

All heads —

Expected heads —

Reading this —

The formula

P(k heads) = C(n, k) × p^k × (1 − p)^(n − k)

This is the binomial distribution. The streak figure uses a separate exact recurrence over sequences that have no such streak.

Change the chance of heads to model a biased coin, or any event with two outcomes.

What is the chance of exactly 5 heads in 10 flips?

24.61% (1 in 4.06). Even the most likely count is not all that likely.

How likely is a streak of 3 heads in 10 flips?

50.78%.

What about 10 heads in a row?

0.09766% (1 in 1,024), from 10 flips. Over 1,000 flips, a streak of at least 10 heads has a 38.54% (1 in 2.59) chance.