Binomial Distribution Calculator
Result
Binomial Distribution Calculator Find the probability of getting exactly k successes — and up to k, and more than k — in n independent trials, each with success probability p. This calculator also reports the mean, variance, and standard deviation of the — free online calculator.
Formula
- Binomial Distribution Calculator calculates its result from Number of Trials (n), Probability of Success (p), Number of Successes (k). It uses the formula P(X=k) = C(n,k) × p^k × (1−p)^(n−k) · μ = n·p · σ = √(n·p·q). Change any input to recalculate the result instantly.
- The main inputs are Number of Trials, Probability of Success, Number of Successes. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Binomial Distribution
- Number of Trials: 10
- Probability of Success: 0.5
- Number of Successes: 4 k
Exact count probability, cumulative and upper-tail probabilities, expected number of successes, standard deviation and variance. Input p is a fraction from 0 to 1; output probabilities are percentages.
Sample result: Calculating…
Frequently asked questions
What does the Binomial Distribution calculate?
Binomial Distribution Calculator Find the probability of getting exactly k successes — and up to k, and more than k — in n independent trials, each with success probability p. This calculator also reports the mean, variance, and standard deviation of the — free online calculator.
Which values should I enter?
Enter Number of Trials, Probability of Success, Number of Successes using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: P(X=k) = C(n,k) × p^k × (1−p)^(n−k) · μ = n·p · σ = √(n·p·q).
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.