Negative Binomial Distribution Calculator

Use this negative binomial distribution calculator to find the probability of needing a specific number of trials to achieve a set number of events. Enter the event probability (p), the number of events (r), and the total number of trials (X). For example, this negative binomial distribution calculator can tell you the probability that you will get 8 heads in 10 coin tosses when the probability of each head is 0.5.

The calculator displays the exact probability as well as cumulative probabilities related to the number of trials you specify. It also shows a negative binomial distribution graph, highlighting the number of trials (X) you specified in red. Each bar in the graph represents the probability of obtaining the number of events (r) in the total number of trials. This visual helps you see how your trial count compares to the distribution of outcomes. Below the negative binomial distribution calculator, you’ll find additional tools and explanations for interpreting the results. See all my Statistical Calculators!

This calculator uses the negative binomial distribution to find the likelihood that the r^th event occurs on the x^th trial.

To learn more about this distribution, how to use it, and its calculations, read my article Negative Binomial Distribution: Uses & Formula. Additionally, other probability distributions for binary data exist, which you use for different reasons. Learn more about them with Binomial and Other Probability Distributions for Binary Data.