Binomial chance explorer

What it does

Calculate and visualise exact, at-least and at-most probabilities for repeated independent trials.

How to use it

1. Enter the trial count, probability per trial and target successes, then calculate the distribution.
2. Processing stays in your browser. No upload or sign-up.

Example

With 20 trials and a 10% success probability, the chance of at least three successes is about 32.3073%.

Methodology

The binomial mass function is calculated using recurrences outward from its mode and normalized, avoiding underflow at the initial tail. Selected probabilities are summed directly.

Limitations

0–1,000 integer trials, 0–100% probability and an integer target from zero to the trial count. Independent trials and constant success probability are assumptions. Finite-precision tails can round to zero; this does not predict an event's underlying probability.

Automation

This tool runs in your browser. No upload API or MCP endpoint is available.