Binomial Probability Calculator
Calculate exactly, at most or at least k successes in n independent trials, with expected value and standard deviation.
Set your values
Adjust the values, then calculate your result.
How to use Binomial Probability Calculator
- Load the included example or provide your own input and settings.
- Choose the operation and review the supported format below.
- Run the tool, inspect the result, and copy or download it.
Choose the probability event precisely
Set the number of trials, the target number of successes and a success probability from zero through one. Exactly counts only the chosen outcome. At most includes that outcome and every smaller count, while at least includes it and every larger count. The report also gives the expected number of successes and standard deviation, which describe the distribution rather than guaranteeing a particular outcome.
Check the binomial assumptions
Trials must be independent and share the same success probability. Sampling without replacement or changing conditions may require another distribution. The calculator supports up to one thousand trials and evaluates probabilities through logarithms rather than overflowing factorials. Very tiny tail probabilities can underflow to zero in floating-point arithmetic. Endpoint probabilities zero and one are handled explicitly, and a target count cannot exceed the number of trials.
Does Binomial Probability Calculator upload my input?
No. This tool processes input locally in your browser without calling a conversion API.
Is input uploaded?
Processing takes place in your browser. This tool does not send your input or selected files to a conversion API.