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Negative Binomial Distribution Calculator

Probability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.

Related tools

All Statistics & probability tools →
Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.Exponential Distribution CalculatorCompute exponential-distribution probabilities for waiting times from the rate λ, including P(X≤x), P(X>x) and a range.Gaussian Distribution GeneratorNormally-distributed numbers via Box–Muller, with an optional seed and the sample mean and SD.Geometric Distribution CalculatorCompute the probability of the first success on trial k (or after k failures) from the per-trial success probability p.Hypergeometric Distribution CalculatorCompute hypergeometric probabilities of drawing k successes in n draws without replacement from a population of N with K successes.Normal Distribution CalculatorCompute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation.Weibull Distribution CalculatorCompute Weibull reliability probabilities F(x) and R(x) for failure analysis from the shape β and scale η.

Negative Binomial Distribution Calculator works straight from this page — free, instant, nothing to install. It sits under Statistics & probability in our catalogue, alongside Binomial Probability Calculator and Beta Distribution Calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Negative Binomial Distribution Calculator do?

Probability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

How is Negative Binomial Distribution Calculator different from Binomial Probability Calculator?

They sit next to each other but answer different questions. Binomial Probability Calculator: get P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Beta Distribution Calculator is the closest one after this: Compute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.

What else is worth having open alongside it?

Exponential Distribution Calculator and Gaussian Distribution Generator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.ExplainerForty Out and Sixty Back Averages Forty-EightThe harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.ExplainerIf the Variance Is Not the Mean, It Is Not PoissonWith an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.ExplainerTurn 30 Into 300 and the Interquartile Range Does Not MoveFor 2, 5, 7, 8, 10, 13, 18, 21, 25, 30 the range is 28, the standard deviation 9.24 and the IQR 13. Replace the last value with 300 and only the IQR survives unchanged.ExplainerThe Expected Value Is a Number That Never HappensOutcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.