Negative Binomial Distribution Calculator
Find the probability that it takes a specific number of trials to reach a target number of successes.
What the negative binomial distribution models
The negative binomial distribution gives the probability that it takes exactly x independent trials to reach a target number of successes, r, when each trial has the same success probability p. It generalizes the geometric distribution, which is the special case where you are waiting for just one success.
How this calculator works
Enter the probability of success on each trial, the number of successes you need, and the total number of trials you want to check. The calculator applies P(X = x) = C(x-1, r-1) × pr × (1-p)x-r, using combinations computed through the gamma function. It also reports the expected number of trials needed (r/p) and the variance of that count.
This distribution assumes every trial is independent with a constant success probability. It is used to model scenarios such as the number of sales calls needed to close a fixed number of deals. This tool is intended for general statistics education.