Fun

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%.

Number of Coins

Results

Click Flip to toss your coins.

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.

Frequently Asked Questions

Is this coin flip fair?
Yes. Each flip uses a random number generator with equal probability of heads or tails. Over thousands of flips, the distribution will converge very close to 50/50.
What are the odds of flipping 10 heads in a row?
The probability is (1/2)^10 = 1/1,024, or about 0.098%. It is rare but absolutely possible. If you flip a coin 1,024 times, you would statistically expect it to happen about once.
Does a previous flip affect the next one?
No. Each flip is completely independent. If you just flipped 5 heads in a row, the next flip still has a 50% chance of heads. The belief that tails is 'due' is called the gambler's fallacy.
Can I use this for making decisions?
Absolutely. A coin flip is a mathematically fair way to make a binary decision. Some research suggests that people who make decisions by coin flip for tough choices report higher satisfaction months later.
How many flips to get close to 50/50?
With 100 flips, you will typically be within 5-10% of 50/50. With 1,000 flips, within 1-3%. With 10,000 flips, within 0.5-1%. The more flips, the closer the ratio converges to the true 50% probability.