Binomial distribution calculator

Calculate exact-count and cumulative probabilities for independent trials with a fixed success probability.

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Number of trials

Success probability per trial

More inputs and assumptions

Successes k

Answer

…

Calculate exact-count and cumulative probabilities for independent trials with a fixed success probability.

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Saved scenario

Save the current answer, then change an input to compare. This clears when you leave.

Formula and assumptions

Trials must be independent and share the same probability. Supports 0 to 1,000 trials. Very tiny probabilities can underflow to zero in browser arithmetic; sampling without replacement needs a different model.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

Scratch calculator

Check another calculation

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Updated 2026-09-26

Using Binomial distribution calculator

Calculate exact-count and cumulative probabilities for independent trials with a fixed success probability.

Next: Basic calculator

A worked example

With number of trials = 10, success probability per trial = 0.5, successes k = 5, the probability of exactly k is 0.24609375.

Before you use the result

Example results for number of trials

These examples use Success probability per trial: 0.5; Successes k: 5. They are reference calculations, not recommended settings.

Number of trials	Probability of exactly k
5	0.03125
10	0.24609375
20	0.0147857666016

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