Skip to Controls Skip to Chart Skip to Results

Binomial Distribution CalculatorStatLens

Trials (n) Probability (p) k value Probability type

Mean (μ = np): — SD (σ = √npq): —

Show mean line Show normal approximation

Probability table

Binomial Distribution Calculator

Finds the probability of a given number of successes in a fixed number of independent trials, each with the same chance of success. The bars show the whole distribution; the highlighted bars are the ones your probability adds up.

Setting up the distribution

Trials (n) — how many trials (e.g. coin flips, patients, at-bats).
Probability (p) — the chance of success on a single trial, between 0 and 1.

The mean (μ = np) and standard deviation (σ = √npq) update automatically below the inputs.

Asking a probability question

k value — the number of successes you are asking about.
Probability type — which question to answer: exactly k P(X = k), or a range: P(X ≤ k), P(X ≥ k), P(X < k), or P(X > k).

The banner above the chart reports the result, and the matching bars are highlighted.

Overlays

Show mean line — marks μ = np on the chart.
Show normal approximation — overlays the normal curve that approximates this binomial. The approximation is good when both np and n(1−p) are large enough (roughly ≥ 10).

Probability table

Expand Probability table below the chart for the exact and cumulative probability of every value of k.

Keyboard shortcuts

?: Show this help
Esc: Close this dialog

New to this tool? Walk through it step by step.

Open guided walkthrough ↗