Binomial Distribution Calculator
How this is calculated
The binomial model applies when there is a fixed number of independent trials, each trial has two outcomes, and the success probability stays constant from trial to trial.
Core formula: P(X = x) = C(n,x)px(1-p)n-x, with C(n,x) = n!/[x!(n-x)!]. Cumulative events are obtained by summing the relevant binomial probabilities. The calculator uses a numerically stable regularized incomplete-beta evaluation for cumulative tails and log-gamma arithmetic for individual probabilities.
This Binomial Distribution Calculator helps researchers, students, analysts, and instructors calculate exact and cumulative binomial probabilities for a fixed number of independent trials. Enter the number of trials, probability of success, and the outcome condition to find probabilities such as exactly, at most, at least, fewer than, more than, or between selected numbers of successes, with live distribution visuals and supporting summary statistics.
