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Probability Calculators

Binomial Probability Calculator

Probability of exactly, at most or at least k successes in n independent trials, with mean and standard deviation.

Enter values

Results update as you type.

Result

P(X = 6)

0.20507813

P(X ≤ 6)
0.828125
P(X ≥ 6)
0.37695312
Mean np
5
Standard deviation
1.581139

About the Binomial Probability Calculator

Probability of exactly, at most or at least k successes in n independent trials, with mean and standard deviation.

Also known as: binomial distribution calculator, binomial pmf, binomial cdf, probability of k successes.

How to use this calculator

  1. Enter trials n, success probability p, successes k.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ

Worked example

Using the values pre-filled in the calculator above:

  • Trials n = 10
  • Success probability p = 0.5
  • Successes k = 6

the calculator returns:

  • P(X = 6): 0.20507813
  • P(X ≤ 6): 0.828125
  • P(X ≥ 6): 0.37695312
  • Mean np: 5