Binomial Probability Calculator
Find the probability of exactly or at most successes with the binomial distribution
How to use
- Enter the number of trials n.
- Enter the success probability p for one trial as a decimal (50% = 0.5).
- Enter the number of successes k.
- The exactly, at most and at least probabilities will show below.
Note: Formula: P(X = k) = C(n, k) x p^k x (1-p)^(n-k). The calculation uses a stable recurrence so it does not overflow even for large n.
Frequently Asked Questions (FAQ)
What does the binomial probability calculator find?
The probability of exactly, at most, or at least k successes in n independent trials with the same chance of success.
What do n, k and p mean in this calculator?
n is the number of trials, k is the number of successes, and p is the probability of success on a single trial, entered as a number from 0 to 1.
What does the “at least k” result mean?
It adds the probabilities of k, k plus 1, and every value up to all n trials succeeding. It answers questions like what is the chance of 5 or more heads in 10 coin tosses.
Does it show the formula it uses?
Yes. The page shows the binomial formula with your numbers filled in, so you can follow each step of the calculation.