Coin Flip
Flip one or multiple coins at once. Track heads and tails with running statistics.
Quick Answer
A fair coin has a 50/50 chance of landing heads or tails on each flip. Over many flips, the ratio converges to 50%.
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About the Coin Flipper
This free coin flipper simulates fair coin tosses using a random number generator. Each flip has an independent 50% chance of landing heads and 50% chance of landing tails. You can flip multiple coins simultaneously and track your running statistics over time to see the law of large numbers in action.
The Law of Large Numbers
If you flip a coin 10 times, you might see 7 heads and 3 tails. That does not mean the coin is unfair. With small sample sizes, deviation from 50/50 is expected and normal. As you increase the number of flips to hundreds or thousands, the observed ratio of heads to tails converges closer and closer to 50%. This fundamental statistical principle is called the law of large numbers.
Coin Flip Probability
Each coin flip is an independent event with two equally likely outcomes. The probability of getting heads on any single flip is always 0.5, regardless of what happened on previous flips. The probability of getting all heads when flipping multiple coins is (0.5)^n, where n is the number of coins. For example, flipping 10 heads in a row has a probability of about 0.1%, or roughly 1 in 1,024.
Uses for Coin Flips
Coin flips are used to make binary decisions, settle disputes fairly, determine who goes first in games, and teach probability concepts. In statistics, the coin flip (Bernoulli trial) is the foundation for understanding binomial distributions, hypothesis testing, and many other concepts. In sports, coin tosses determine which team kicks off or chooses sides.