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Binomial distribution calculator

The binomial distribution calculator returns exact probabilities and quantiles for the number of successes in n independent trials with success probability p.

What is Binomial distribution calculator?

The binomial counts successes in a fixed number of independent trials with a constant success probability — the model behind an exact test of a proportion and behind sample-size arithmetic for binary endpoints.

Because the support is discrete, P(X ≤ k), P(X < k), P(X ≥ k) and P(X > k) are four different numbers, and choosing the wrong one is the usual source of off-by-one errors. All four are reported.

When should I use Binomial distribution calculator?

Finding the exact probability of at least k successes.
Checking a p-value from an exact binomial test.
Reading a critical count for a decision rule.

What data does it need?

Distribution parameters, plus a value x, a tail probability p, or both.

What does it report?

For x: the density or exact probability and each tail. For p: the lower, upper and two-tailed critical values.

What does it assume?

None — this evaluates a distribution rather than testing data against one.