Binomial Probability Calculator

About this calculator

For n independent trials each with success probability p, this calculator computes P(X=k) = C(n,k) × p^k × (1−p)^(n−k) — the binomial probability mass function — for an exact number of successes, and sums it across values to get P(X≥k) or P(X≤k) for at-least or at-most probabilities.

It's the standard model whenever an outcome is binary and trials are independent with a fixed success rate: quality control engineers use it to find the probability of k defective units in a batch, geneticists apply it to Mendelian inheritance ratios, pollsters and A/B testers use it to judge whether an observed split could plausibly arise by chance, and it's a core topic in every introductory statistics course.