Binomial Distribution Calculator
Calculate the probability of observing a number of successes in independent binary trials.
Why use this calculator
Model a fixed number of yes-or-no outcomes
The binomial distribution describes the number of successes across a fixed number of independent trials when every trial has the same success probability. It is useful for conversion-like outcomes, quality checks, and simple event counts.
What is a binomial distribution?
A binomial random variable counts successes in n independent trials, where each trial has the same probability p of success. Its expected number of successes is n × p and its standard deviation is √(n × p × (1 − p)).
Unlike a normal distribution, a binomial distribution is discrete: it assigns probability to 0, 1, 2, and other whole success counts, not to every value on a continuous scale.
Using binomial probabilities in A/B testing
A conversion is a binary outcome
For one fixed variant with a stable conversion probability, the number of conversions is naturally modeled as binomial. Comparing two conversion rates requires a two-group procedure rather than treating each result in isolation.
Check independence and a stable probability
Repeat visitors, clustered assignment, time trends, and targeting can make outcomes dependent or change the probability across users. Those situations need a model that accounts for the design.
Use exact probabilities for counts
Normal approximations can be useful at large sample sizes, but the exact binomial calculation is especially helpful for small counts or rare outcomes.