Negative Binomial Distribution Calculator
Probability of the rth success on the nth trial.
Enter your values
Enter the target number of successes r you are working with.
Enter the success probability p you are working with.
Enter the trial number n you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- P(N = n)
- 12.4416%
- Expected trials for r successes
- 7.5
- Parameters
- r=3, p=0.4, n=7
Quick answer
The negative binomial distribution gives the probability of needing exactly n trials to get r successes, each trial succeeding with probability p.
P(N=n) = C(n-1, r-1) p^r (1-p)^(n-r)
At a glance
| What it does | Probability of the rth success on the nth trial. |
|---|---|
| Category | Statistics |
| Inputs needed | Target number of successes r, Success probability p, Trial number n |
| Main output | P(N = n) |
| Formula | P(N=n) = C(n-1, r-1) p^r (1-p)^(n-r) |
| Cost | Free — no sign-up, no download |
How to use the Negative Binomial Distribution Calculator
- 1Enter the target number of successes r.
- 2Enter the per-trial success probability p.
- 3Enter the trial number n on which the rth success should occur.
Inputs explained
- Target number of successes r
- Enter the target number of successes r you are working with.
- Success probability p
- Enter the success probability p you are working with.
- Trial number n
- Enter the trial number n you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Target number of successes r3
- Success probability p0.4
- Trial number n7
Results
- P(N = n)12.4416%
- Expected trials for r successes7.5
- Parametersr=3, p=0.4, n=7
Frequently asked questions
How is this different from binomial?
Binomial fixes the number of trials and counts successes; negative binomial fixes the number of successes and finds the trial count.
What is the expected number of trials?
On average, r/p trials are needed to reach r successes.
What do I need to enter into the Negative Binomial Distribution Calculator?
Just 3 values: target number of successes r, success probability p, trial number n. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Negative Binomial Distribution Calculator work out the answer?
The negative binomial distribution gives the probability of needing exactly n trials to get r successes, each trial succeeding with probability p. It applies the formula P(N=n) = C(n-1, r-1) p^r (1-p)^(n-r) and shows the working so you can check each step by hand.
Is the Negative Binomial Distribution Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.