Coin Flip Probability Calculator

How it is calculated

For a fair coin the chance of exactly k heads in n flips is P = C(n, k) × 0.5n, where C(n, k) = n! ÷ (k! × (n − k)!) counts the ways to choose which flips are heads. The tool also reports the probability of one specific sequence, such as HTHHT, which is always 0.5n. Flips and heads must be whole numbers, flips between 1 and 1000, and heads between 0 and flips. The exact-heads figure is a percentage with two decimals; the sequence probability is a decimal with eight places, so it shows 0.00000000 once n is 28 or more, although it is not truly zero. Each flip is assumed fair and independent of the others.

Common mistakes

• Expecting an even split to be likely. Exactly 5 heads in 10 flips is only 24.61%, and the chance of an exact half falls further as n grows (2.52% for 500 heads in 1000).
• Confusing "exactly k heads" with "at least k heads". This tool gives only the exact count; to get at least k you must add the probabilities for k, k + 1, ... n.
• Believing a streak makes the opposite side due. Each flip is independent, so after 5 heads in a row the next flip is still 50/50.
• Comparing the two outputs as if they were the same thing. One specific sequence is far less likely than the count of heads, because many sequences share the same count.
• Entering a decimal or more than 1000 flips, which the tool rejects.