Statistics & Probability

Instant, private, and free

Coin Flip Probability Calculator.

Calculate the probability of exactly k heads in n independent flips.

On-device calculationNo signup
01

Set your values

Results update as you type.

Probability: 0.246094

Probability

0.246094
Percent: 24.609375

Percent

24.609375

Results update automatically as you type.

Use Cases

Check fairness of a coin

Use the calculator to see how likely it is to get a certain number of heads in a given number of flips, which can help assess if a coin appears fair.

Example: If you flip a coin 10 times and get 8 heads, the calculator shows the probability of that happening with a fair coin.

Plan for games or experiments

Before running a game or experiment involving coin flips, you can estimate the probability of specific outcomes to set expectations.

Example: Calculate the chance of getting at least 5 heads in 10 flips to decide if a game is balanced.

Frequently Asked Questions

How does the coin flip probability calculator work?
It uses the binomial probability formula to compute the likelihood of getting exactly the number of heads you specify out of the total number of flips, given the probability of heads on a single flip (default 0.5).
What inputs do I need to provide?
You need to enter the total number of flips, the number of heads you want to calculate the probability for, and the probability of heads on a single flip (as a decimal between 0 and 1).
Can I use this calculator for biased coins?
Yes, you can adjust the 'Heads probability' field to any value between 0 and 1, allowing you to calculate probabilities for biased coins as well.

Tips & Common Mistakes

Tips

  • Ensure the number of heads is not greater than the number of flips, as that is impossible.
  • For the probability of getting at least a certain number of heads, you can sum the probabilities for that number and all higher numbers.
  • Remember that the probability of heads on a single flip must be between 0 and 1; use 0.5 for a fair coin.
  • Use the debounced results to see updates as you type without needing to press a button.

Common Mistakes to Avoid

  • Entering a number of heads greater than the number of flips, which yields an error or zero probability.
  • Using a percentage (like 50) instead of a decimal (0.5) for the heads probability.
  • Forgetting that the calculator gives the probability of exactly the specified number of heads, not 'at least' or 'at most'.

Last updated: August 13, 2026