Negative binomial distribution calculator
Find the probability of failures before the r-th success or total trials to that success. See the CDF, mean and variance.
How do I use this page?
- Load an example or enter your own data.
- Choose the calculation type and units where available.
- Read the result, additional measures and substituted formula.
What this page does not do: Trials must be independent with a constant p greater than zero. r: 1–1000, x: 0–10,000. Very small probabilities may round to zero. This model does not predict the next lottery draw.
Further reading
Formula
P(K=k) = C(k+r−1,k) pʳ (1−p)ᵏ Theory — what is the negative binomial distribution?
This distribution models independent trials with a constant success probability p, repeated until the r-th success occurs. K counts the failures before that final success, and the total number of trials T = K + r also includes the successes, with the last trial always a success. The calculator returns the CDF, mean and variance for given r and p. For r = 3 and p = 0.5, the probability of exactly two failures is 18.75%, and of at most two failures is 50%.
Frequently asked questions
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What should I check before interpreting the result?
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