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Binomial Calculator

Compute combinations (nCr), permutations (nPr), and binomial probabilities P(X=k), P(X≤k), and P(X≥k) for discrete probability questions.

Combinations & permutations

Combinations nCr
120
Permutations nPr
720
nCr calculatorcombinations and permutations calculator

Binomial probabilities

Enter as a decimal between 0 and 1.
P(X = k)
0.266828
P(X <= k)
0.649611
P(X >= k)
0.617217

How to use this tool

  1. Use the top card to compute nCr combinations and nPr permutations from integers n and r.
  2. Enter n, p, and k in the binomial panel to compute binomial probabilities.
  3. Interpret P(X = k), P(X <= k), and P(X >= k) in the context of your probability question.

Binomial probability calculator for quick checks

  • Avoid manual binomial coefficient calculations when checking exam answers.
  • Use nCr as a combinations calculator and nPr as a permutations calculator.
  • See exact, cumulative, and at-least probabilities for the binomial distribution.

What this binomial calculator assumes

  • Trials are independent with a constant probability of success p.
  • The random variable X counts the number of successes in n trials.
  • Probabilities are computed directly from the binomial formula with combinations nCr.

FAQ

What is the difference between combinations (nCr) and permutations (nPr)?
Combinations nCr count selections where order does not matter. Permutations nPr count ordered arrangements of r items from n.
Can I enter percentages for p instead of decimals?
Enter p as a decimal between 0 and 1 (for example, 0.3 instead of 30%). This keeps the binomial formula consistent.
Why do very extreme probabilities show as 0?
For large n or very small probabilities, rounding to 6 decimal places may show tiny probabilities as 0. The underlying calculation still uses full floating-point precision.

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