coin flip probability

Coin Flip Probability Calculator

Choose the number of flips, a heads target, and a streak length. Compare events that sound similar but have different probabilities.

Assumes independent flips with a 50% chance of each side. Inputs are limited to 1–500 flips; heads may be zero.

Exactly 5 heads in 1024.61%
At least 5 heads in 1062.30%
At most 5 heads in 1062.30%
Next 3 flips are all heads12.50%
Next 3 flips are all heads OR all tails25.00%
At least 3 consecutive heads anywhere in 10 flips50.78%
At least 3 matching sides anywhere in 10 flips82.62%

How to interpret the answer

Exactly k heads in n flips uses C(n,k) × (1/2)ⁿ, where C(n,k) counts the possible positions of those heads. “At least” and “at most” add the relevant exact probabilities.

For two flips, HH has probability 25%. Either HH or TT has probability 50%. In three flips, HH appears in HHH, HHT, and THH, giving 3/8 = 37.5% for consecutive heads anywhere in the session.

The streak calculation tracks unfinished runs after each flip and counts each successful sequence once, including overlapping runs. Small probabilities use scientific notation with a percent sign.

Choose the event before calculating

Exactly five heads in ten flips allows the heads to occur in any five positions. Five consecutive heads is a restriction on order. These are different questions, even though both mention five heads.

For a specific block of r flips, all heads has probability 2⁻ʳ. Either all heads or all tails has probability 2 × 2⁻ʳ for r ≥ 1. A streak somewhere in a longer sequence has more possible starting points, and overlaps must be counted only once.

Copy a calculator link to preserve the input settings. Those settings live in the URL fragment and do not create a new search landing page. All results assume a fair coin and independent trials.

Questions about coin flip probability calculator

No. It calculates probabilities from the fair-coin model. Use the simulator to observe a randomly generated sample.