Calculadora de Probabilidade de Lançamento de Moeda
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P = C(n,k) · 0,5ⁿ
About this calculator
The Coin Toss Probability Calculator is an online tool that computes the probability of getting a specific number of heads (k) in a series of tosses of a fair coin (n). It uses the binomial distribution with success probability p = 0.5, assuming the coin is unbiased. The result is given as a percentage, making it easy to interpret.
The calculation is based on the binomial formula: P = C(n,k) · 0.5ⁿ, where C(n,k) is the binomial coefficient (number of combinations of n items taken k at a time). The tool automatically performs the calculation; you just need to enter the total number of tosses (n) and the desired number of heads (k). For example, for 10 tosses and 6 heads, the probability is approximately 20.51%.
This calculator is useful in various situations, such as probability studies, gambling, statistical simulations, or personal curiosity. For instance, you can check the probability of getting exactly 5 heads in 10 tosses (about 24.61%) or at least 8 heads in 10 tosses (5.47%).
Important caveats: the calculator assumes a fair coin (p=0.5) and independent tosses. If the coin is biased, the result will be inaccurate. Also, for large n (above 1000), the calculation may require significant computational resources; the tool may limit n to ensure performance.
Frequently asked questions
Does the calculator work for biased coins?
No. This calculator assumes a fair coin with 50% probability for each side. For biased coins, you need a binomial distribution calculator with a custom p.
What is the probability of getting at least 3 heads in 5 tosses?
The probability of at least 3 heads is the sum of probabilities of 3, 4, and 5 heads. Using the calculator, compute each and add. For 5 tosses, the result is 50%.
Can I use the calculator for tails probabilities?
Yes. Since the coin has two sides, the probability of getting k tails is the same as getting k heads, because p=0.5. Just consider tails as success.
What does the binomial coefficient C(n,k) mean?
C(n,k) represents the number of ways to choose k items from a set of n, without considering order. In the formula, it counts the different sequences of tosses that result in exactly k heads.
Is there a limit on n?
Yes, to prevent crashes, the maximum n is 1000. For n above that, the calculation may be too heavy or result in extremely small numbers.